Stochastic RAG: blame over 200 test cases

rewrite → retrieve → answer → verify; every step is a mocked LLM sampling from logits via the Gumbel-max trick. Fixes are stronger models / a reranker / a grounding check.

Counterfactual blame (recorded noise)

200 cases run, 154 failures, 154 analyzed, 20 not fixable by any combination of fixes. Cost 6017. all failures analyzed.

{'mode': 'recorded', 'n_worlds': 1, 'crn': True, 'method': 'auto', 'ci': 'normal', 'delta': 0.05}

stepfixing this step alone resolvesmean Shapley blame (±CI)sharelast-touch
retrieve26.0%
+0.319
36.7%2
rewrite27.3%
+0.312
35.8%0
answer16.2%
+0.181
20.8%0
verify5.2%
+0.058
6.7%149
Per-case drill-down
q000 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 0'
'synthetic question 0'
difficulty
0.637
0.637
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q001 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 15; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 1'
'synthetic question 1'
difficulty
0.27
0.27
rewrite
'precise'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q004 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 4'
'synthetic question 4'
difficulty
0.813
0.813
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q005 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.167
retrieve+0.000+0.000+0.167
answer+1.000+0.000+0.667
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 5'
'synthetic question 5'
difficulty
0.913
0.913
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q006 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 24; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 6'
'synthetic question 6'
difficulty
0.607
0.607
rewrite
'vague'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q007 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 7'
'synthetic question 7'
difficulty
0.729
0.729
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q008 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.500
answer+0.000+1.000+0.500
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 8'
'synthetic question 8'
difficulty
0.544
0.544
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q009 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.500
answer+0.000+1.000+0.500
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 9'
'synthetic question 9'
difficulty
0.935
0.935
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q010 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 10'
'synthetic question 10'
difficulty
0.816
0.816
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q011 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 21; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 11'
'synthetic question 11'
difficulty
0.003
0.003
rewrite
'vague'
'precise'
retrieve
'stale'
'stale'
answer
'stale_fact'
'stale_fact'
verify
'stale_fact'
'abstain'
q012 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 52; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 12'
'synthetic question 12'
difficulty
0.857
0.857
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q013 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 13'
'synthetic question 13'
difficulty
0.034
0.034
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q014 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 14'
'synthetic question 14'
difficulty
0.73
0.73
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q015 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 24; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 15'
'synthetic question 15'
difficulty
0.176
0.176
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q016 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 16'
'synthetic question 16'
difficulty
0.863
0.863
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q017 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 17'
'synthetic question 17'
difficulty
0.541
0.541
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q018 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 18'
'synthetic question 18'
difficulty
0.3
0.3
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q019 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 19'
'synthetic question 19'
difficulty
0.423
0.423
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q022 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 22'
'synthetic question 22'
difficulty
0.671
0.671
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q023 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 49; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 23'
'synthetic question 23'
difficulty
0.647
0.647
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q025 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 25'
'synthetic question 25'
difficulty
0.384
0.384
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q026 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 26'
'synthetic question 26'
difficulty
0.997
0.997
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q027 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 27'
'synthetic question 27'
difficulty
0.981
0.981
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'stale_fact'
verify
'hallucinated'
'abstain'
q029 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 29'
'synthetic question 29'
difficulty
0.65
0.65
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q030 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.667
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 30'
'synthetic question 30'
difficulty
0.688
0.688
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q031 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 31'
'synthetic question 31'
difficulty
0.389
0.389
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q032 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 32'
'synthetic question 32'
difficulty
0.135
0.135
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q033 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.667
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 33'
'synthetic question 33'
difficulty
0.721
0.721
rewrite
'vague'
'vague'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q034 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.667
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 34'
'synthetic question 34'
difficulty
0.525
0.525
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q036 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 36'
'synthetic question 36'
difficulty
0.486
0.486
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q037 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 37'
'synthetic question 37'
difficulty
0.889
0.889
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q038 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 38'
'synthetic question 38'
difficulty
0.934
0.934
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q039 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 26; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 39'
'synthetic question 39'
difficulty
0.358
0.358
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q040 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 40'
'synthetic question 40'
difficulty
0.572
0.572
rewrite
'vague'
'vague'
retrieve
'stale'
'stale'
answer
'stale_fact'
'abstain'
verify
'stale_fact'
'abstain'
q041 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 41'
'synthetic question 41'
difficulty
0.322
0.322
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q042 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 46; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 42'
'synthetic question 42'
difficulty
0.594
0.594
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q043 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 43'
'synthetic question 43'
difficulty
0.338
0.338
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q044 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.250
retrieve+0.000+0.000+0.250
answer+0.000+0.000+0.250
verify+0.000+0.000+0.250
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 44'
'synthetic question 44'
difficulty
0.392
0.392
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q045 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 24; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 45'
'synthetic question 45'
difficulty
0.89
0.89
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q046 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 46'
'synthetic question 46'
difficulty
0.227
0.227
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q047 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 26; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 47'
'synthetic question 47'
difficulty
0.623
0.623
rewrite
'vague'
'vague'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q048 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 48'
'synthetic question 48'
difficulty
0.084
0.084
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q050 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.667
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 50'
'synthetic question 50'
difficulty
0.787
0.787
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q052 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 21; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 52'
'synthetic question 52'
difficulty
0.876
0.876
rewrite
'wrong_entity'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'stale_fact'
'stale_fact'
verify
'stale_fact'
'abstain'
q053 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+0.000+0.500
answer+1.000+0.000+0.500
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 53'
'synthetic question 53'
difficulty
0.059
0.059
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q054 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 54'
'synthetic question 54'
difficulty
0.336
0.336
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q055 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 52; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 55'
'synthetic question 55'
difficulty
0.15
0.15
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q056 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 56'
'synthetic question 56'
difficulty
0.45
0.45
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q057 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 57; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 57'
'synthetic question 57'
difficulty
0.796
0.796
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q058 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 43; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 58'
'synthetic question 58'
difficulty
0.231
0.231
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q059 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 59'
'synthetic question 59'
difficulty
0.052
0.052
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q060 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 60'
'synthetic question 60'
difficulty
0.405
0.405
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q061 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 61'
'synthetic question 61'
difficulty
0.199
0.199
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q062 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 62'
'synthetic question 62'
difficulty
0.091
0.091
rewrite
'precise'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q063 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 46; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 63'
'synthetic question 63'
difficulty
0.58
0.58
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q064 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 43; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 64'
'synthetic question 64'
difficulty
0.299
0.299
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q066 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 66'
'synthetic question 66'
difficulty
0.2
0.2
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q067 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 49; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 67'
'synthetic question 67'
difficulty
0.942
0.942
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q068 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 68'
'synthetic question 68'
difficulty
0.365
0.365
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q069 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 69'
'synthetic question 69'
difficulty
0.105
0.105
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q070 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+1.000+0.500
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 70'
'synthetic question 70'
difficulty
0.629
0.629
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q071 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 43; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 71'
'synthetic question 71'
difficulty
0.927
0.927
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q072 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.333
retrieve+1.000+0.000+0.333
answer+1.000+0.000+0.333
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 72'
'synthetic question 72'
difficulty
0.44
0.44
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q073 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 46; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 73'
'synthetic question 73'
difficulty
0.955
0.955
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q074 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 46; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 74'
'synthetic question 74'
difficulty
0.5
0.5
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q075 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.167
retrieve+0.000+1.000+0.667
answer+0.000+0.000+0.167
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 46; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 75'
'synthetic question 75'
difficulty
0.425
0.425
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q077 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 77'
'synthetic question 77'
difficulty
0.995
0.995
rewrite
'vague'
'vague'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q078 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.250
retrieve+0.000+0.000+0.250
answer+0.000+0.000+0.250
verify+0.000+0.000+0.250
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 78'
'synthetic question 78'
difficulty
0.949
0.949
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q079 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 79'
'synthetic question 79'
difficulty
0.46
0.46
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q083 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 46; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 83'
'synthetic question 83'
difficulty
0.786
0.786
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q086 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 86'
'synthetic question 86'
difficulty
0.711
0.711
rewrite
'wrong_entity'
'vague'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q089 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.167
retrieve+0.000+0.000+0.167
answer+0.000+1.000+0.667
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 89'
'synthetic question 89'
difficulty
0.729
0.729
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q090 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 24; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 90'
'synthetic question 90'
difficulty
0.927
0.927
rewrite
'wrong_entity'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q091 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 91'
'synthetic question 91'
difficulty
0.968
0.968
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q093 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 93'
'synthetic question 93'
difficulty
0.864
0.864
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q094 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 94'
'synthetic question 94'
difficulty
0.981
0.981
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q095 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 95'
'synthetic question 95'
difficulty
0.957
0.957
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q096 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 96'
'synthetic question 96'
difficulty
0.149
0.149
rewrite
'vague'
'vague'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q098 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 98'
'synthetic question 98'
difficulty
0.89
0.89
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q099 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
◆
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 99'
'synthetic question 99'
difficulty
0.822
0.822
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'near_miss'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q100 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.500
answer+0.000+1.000+0.500
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 100'
'synthetic question 100'
difficulty
0.48
0.48
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q101 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 101'
'synthetic question 101'
difficulty
0.232
0.232
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q102 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 102'
'synthetic question 102'
difficulty
0.802
0.802
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q103 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 103'
'synthetic question 103'
difficulty
0.924
0.924
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q104 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.667
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 104'
'synthetic question 104'
difficulty
0.266
0.266
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q105 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 24; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 105'
'synthetic question 105'
difficulty
0.539
0.539
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q107 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 107'
'synthetic question 107'
difficulty
0.931
0.931
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q108 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 108'
'synthetic question 108'
difficulty
0.041
0.041
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q109 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 109'
'synthetic question 109'
difficulty
0.732
0.732
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q110 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 110'
'synthetic question 110'
difficulty
0.614
0.614
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q111 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.667
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 111'
'synthetic question 111'
difficulty
0.028
0.028
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q113 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.167
retrieve+0.000+0.000+0.167
answer+1.000+0.000+0.667
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 113'
'synthetic question 113'
difficulty
0.016
0.016
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q115 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 115'
'synthetic question 115'
difficulty
0.513
0.513
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q116 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 15; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 116'
'synthetic question 116'
difficulty
0.929
0.929
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'stale_fact'
'stale_fact'
verify
'stale_fact'
'abstain'
q117 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 117'
'synthetic question 117'
difficulty
0.066
0.066
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q118 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.667
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 118'
'synthetic question 118'
difficulty
0.841
0.841
rewrite
'vague'
'vague'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q120 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.500
answer+0.000+1.000+0.500
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 120'
'synthetic question 120'
difficulty
0.344
0.344
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q121 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 26; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 121'
'synthetic question 121'
difficulty
0.43
0.43
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q122 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.417
retrieve+0.000+1.000+0.417
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 122'
'synthetic question 122'
difficulty
0.966
0.966
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q123 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 26; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 123'
'synthetic question 123'
difficulty
0.562
0.562
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q124 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 15; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 124'
'synthetic question 124'
difficulty
0.259
0.259
rewrite
'precise'
'precise'
retrieve
'stale'
'stale'
answer
'stale_fact'
'stale_fact'
verify
'stale_fact'
'abstain'
q126 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 126'
'synthetic question 126'
difficulty
0.888
0.888
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q127 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+1.000+0.500
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 127'
'synthetic question 127'
difficulty
0.226
0.226
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'hallucinated'
verify
'stale_fact'
'correct'
q128 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 128'
'synthetic question 128'
difficulty
0.125
0.125
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q129 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 129'
'synthetic question 129'
difficulty
0.288
0.288
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q130 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 130'
'synthetic question 130'
difficulty
0.586
0.586
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q131 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 131'
'synthetic question 131'
difficulty
0.554
0.554
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q132 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 132'
'synthetic question 132'
difficulty
0.81
0.81
rewrite
'precise'
'precise'
retrieve
'stale'
'stale'
answer
'stale_fact'
'abstain'
verify
'stale_fact'
'abstain'
q133 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 49; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 133'
'synthetic question 133'
difficulty
0.56
0.56
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q135 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 135'
'synthetic question 135'
difficulty
0.413
0.413
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q136 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 136'
'synthetic question 136'
difficulty
0.818
0.818
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q137 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 137'
'synthetic question 137'
difficulty
0.627
0.627
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q140 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 15; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 140'
'synthetic question 140'
difficulty
0.553
0.553
rewrite
'vague'
'vague'
retrieve
'irrelevant'
'irrelevant'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q142 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.667
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 142'
'synthetic question 142'
difficulty
0.848
0.848
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q143 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 143'
'synthetic question 143'
difficulty
0.145
0.145
rewrite
'precise'
'precise'
retrieve
'stale'
'near_miss'
answer
'stale_fact'
'hallucinated'
verify
'stale_fact'
'abstain'
q145 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 145'
'synthetic question 145'
difficulty
0.91
0.91
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q146 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 146'
'synthetic question 146'
difficulty
0.043
0.043
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q148 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 148'
'synthetic question 148'
difficulty
0.415
0.415
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q150 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 150'
'synthetic question 150'
difficulty
0.01
0.01
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q151 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 151'
'synthetic question 151'
difficulty
0.365
0.365
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q153 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 153'
'synthetic question 153'
difficulty
0.653
0.653
rewrite
'vague'
'vague'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q155 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.667
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 155'
'synthetic question 155'
difficulty
0.703
0.703
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q156 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 156'
'synthetic question 156'
difficulty
0.944
0.944
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q158 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 26; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 158'
'synthetic question 158'
difficulty
0.865
0.865
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q159 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 159'
'synthetic question 159'
difficulty
0.059
0.059
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q162 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.333
retrieve+1.000+0.000+0.333
answer+1.000+0.000+0.333
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 162'
'synthetic question 162'
difficulty
0.489
0.489
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q163 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
◆
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 163'
'synthetic question 163'
difficulty
0.976
0.976
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q165 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.167
retrieve+0.000+0.000+0.167
answer+0.000+1.000+0.667
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 165'
'synthetic question 165'
difficulty
0.309
0.309
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q166 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 166'
'synthetic question 166'
difficulty
0.27
0.27
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q167 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.667
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 167'
'synthetic question 167'
difficulty
0.863
0.863
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q169 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 15; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 169'
'synthetic question 169'
difficulty
0.511
0.511
rewrite
'precise'
'precise'
retrieve
'irrelevant'
'irrelevant'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q170 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.500
answer+0.000+1.000+0.500
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 170'
'synthetic question 170'
difficulty
0.344
0.344
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q171 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 24; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 171'
'synthetic question 171'
difficulty
0.995
0.995
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q172 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 172'
'synthetic question 172'
difficulty
0.316
0.316
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q173 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 24; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 173'
'synthetic question 173'
difficulty
0.183
0.183
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q174 factual=0, v(∅)=0.00, v(all)=0.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 174'
'synthetic question 174'
difficulty
0.88
0.88
rewrite
'precise'
'precise'
retrieve
'irrelevant'
'irrelevant'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q175 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.500
answer+0.000+1.000+0.500
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 175'
'synthetic question 175'
difficulty
0.812
0.812
rewrite
'vague'
'vague'
retrieve
'stale'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q176 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 176'
'synthetic question 176'
difficulty
0.668
0.668
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q177 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+0.000+0.000
answer+0.000+1.000+0.500
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 38; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 177'
'synthetic question 177'
difficulty
0.958
0.958
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q178 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.667
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 178'
'synthetic question 178'
difficulty
0.926
0.926
rewrite
'vague'
'vague'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q179 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 179'
'synthetic question 179'
difficulty
0.748
0.748
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q181 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 181'
'synthetic question 181'
difficulty
0.247
0.247
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q182 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 182'
'synthetic question 182'
difficulty
0.141
0.141
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q183 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 46; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 183'
'synthetic question 183'
difficulty
0.67
0.67
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q184 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+1.000+0.667
answer+0.000+0.000+0.167
verify+0.000+0.000+0.167
◆

exact; 16 coalitions; cost 29; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 184'
'synthetic question 184'
difficulty
0.715
0.715
rewrite
'vague'
'vague'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q185 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+1.000+1.000
retrieve+0.000+0.000+0.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 185'
'synthetic question 185'
difficulty
0.167
0.167
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q187 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+1.000+0.000+0.500
retrieve+1.000+0.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}1.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 187'
'synthetic question 187'
difficulty
0.91
0.91
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q188 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.333
retrieve+0.000+1.000+0.333
answer+0.000+0.000+0.000
verify+0.000+1.000+0.333
◆

exact; 16 coalitions; cost 35; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 188'
'synthetic question 188'
difficulty
0.561
0.561
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q191 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+1.000+1.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 18; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 191'
'synthetic question 191'
difficulty
0.526
0.526
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q192 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+1.000+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 32; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 192'
'synthetic question 192'
difficulty
0.523
0.523
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'

… 4 more cases omitted.

Counterfactual blame (abducted posterior noise)

200 cases run, 154 failures, 154 analyzed, 0 not fixable by any combination of fixes. Cost 45494. all failures analyzed.

{'mode': 'posterior', 'n_worlds': 8, 'crn': True, 'method': 'auto', 'ci': 'normal', 'delta': 0.05}

stepfixing this step alone resolvesmean Shapley blame (±CI)sharelast-touch
retrieve23.1%
+0.316
36.9%5
rewrite19.9%
+0.277
32.4%1
answer15.3%
+0.186
21.7%0
verify6.1%
+0.077
9.0%142
Per-case drill-down
q000 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.146
retrieve+0.125+0.625+0.417
answer+0.000+0.125+0.146
verify+0.000+0.250+0.167
◆

exact; 16 coalitions; cost 313; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.125
{rewrite, retrieve}0.125
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 0'
'synthetic question 0'
difficulty
0.637
0.637
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q001 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.375+0.750+0.562
answer+0.000+0.375+0.188
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 254; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.375
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.375
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 1'
'synthetic question 1'
difficulty
0.27
0.27
rewrite
'precise'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q004 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.625+0.344
retrieve+0.000+0.625+0.281
answer+0.125+0.000+0.094
verify+0.000+0.250+0.156
◆

exact; 16 coalitions; cost 325; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.125
{rewrite, answer}0.125
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 4'
'synthetic question 4'
difficulty
0.813
0.813
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q005 factual=0, v(∅)=0.00, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.271
retrieve+0.250+0.250+0.271
answer+0.375+0.125+0.292
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 291; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 5'
'synthetic question 5'
difficulty
0.913
0.913
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q006 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.292
retrieve+0.125+0.500+0.354
answer+0.125+0.125+0.229
verify+0.000+0.125+0.125
◆

exact; 16 coalitions; cost 325; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.125
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 6'
'synthetic question 6'
difficulty
0.607
0.607
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q007 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.875+0.458
retrieve+0.000+0.625+0.271
answer+0.000+0.125+0.042
verify+0.000+0.250+0.104
◆

exact; 16 coalitions; cost 308; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.125
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 7'
'synthetic question 7'
difficulty
0.729
0.729
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q008 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.365
retrieve+0.500+0.250+0.427
answer+0.000+0.125+0.135
verify+0.000+0.000+0.073
◆

exact; 16 coalitions; cost 339; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 8'
'synthetic question 8'
difficulty
0.544
0.544
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q009 factual=0, v(∅)=0.00, v(all)=0.25, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.125+0.250+0.188
◆
answer+0.000+0.125+0.062
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 215; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.125
{rewrite, retrieve}0.125
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.250
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.125
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.250

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 9'
'synthetic question 9'
difficulty
0.935
0.935
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q010 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.625+0.312
retrieve+0.000+0.500+0.250
answer+0.000+0.250+0.146
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 300; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.500
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 10'
'synthetic question 10'
difficulty
0.816
0.816
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q011 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.375+0.375+0.375
answer+0.125+0.375+0.250
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 294; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.375
{rewrite, retrieve}0.375
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.375
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 11'
'synthetic question 11'
difficulty
0.003
0.003
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q012 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.625+0.531
retrieve+0.125+0.250+0.198
answer+0.000+0.125+0.115
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 359; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.125
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 12'
'synthetic question 12'
difficulty
0.857
0.857
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q013 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+1.000+1.000+1.000
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 262; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 13'
'synthetic question 13'
difficulty
0.034
0.034
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q014 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.271
retrieve+0.125+0.375+0.271
answer+0.000+0.375+0.208
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 296; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.375
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 14'
'synthetic question 14'
difficulty
0.73
0.73
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q015 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.000+0.500
verify+1.000+0.000+0.500
◆

exact; 16 coalitions; cost 222; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}1.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 15'
'synthetic question 15'
difficulty
0.176
0.176
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q016 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.167
retrieve+0.625+0.625+0.625
answer+0.000+0.125+0.062
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 287; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 16'
'synthetic question 16'
difficulty
0.863
0.863
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q017 factual=0, v(∅)=0.00, v(all)=0.75, top: verify
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.500+0.000+0.250
verify+0.750+0.250+0.500
◆

exact; 16 coalitions; cost 180; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.500
{rewrite, answer}0.500
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.500
{verify}0.750
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.750
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 17'
'synthetic question 17'
difficulty
0.541
0.541
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'stale_fact'
verify
'stale_fact'
'abstain'
q018 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.271
retrieve+0.250+0.375+0.333
answer+0.000+0.250+0.146
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 287; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.500
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 18'
'synthetic question 18'
difficulty
0.3
0.3
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q019 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.219
retrieve+0.375+0.625+0.531
answer+0.000+0.125+0.094
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 304; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 19'
'synthetic question 19'
difficulty
0.423
0.423
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q022 factual=0, v(∅)=0.00, v(all)=0.50, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.188
retrieve+0.250+0.125+0.188
answer+0.000+0.250+0.125
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 248; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.500
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.250
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.500

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 22'
'synthetic question 22'
difficulty
0.671
0.671
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q023 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.625+0.469
retrieve+0.125+0.375+0.281
answer+0.000+0.000+0.094
verify+0.000+0.125+0.156
◆

exact; 16 coalitions; cost 347; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.375
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 23'
'synthetic question 23'
difficulty
0.647
0.647
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'stale_fact'
verify
'stale_fact'
'correct'
q025 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.750+0.625+0.667
retrieve+0.375+0.125+0.229
answer+0.000+0.250+0.104
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 321; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.750
{retrieve}0.375
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.875
{retrieve, answer}0.375
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.750
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 25'
'synthetic question 25'
difficulty
0.384
0.384
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q026 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.750+0.625+0.688
retrieve+0.250+0.125+0.188
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 331; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.750
{retrieve}0.250
{rewrite, retrieve}0.875
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.750
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 26'
'synthetic question 26'
difficulty
0.997
0.997
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q027 factual=0, v(∅)=0.00, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.219
retrieve+0.125+0.375+0.281
answer+0.000+0.000+0.031
verify+0.000+0.125+0.094
◆

exact; 16 coalitions; cost 259; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.500
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 27'
'synthetic question 27'
difficulty
0.981
0.981
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'abstain'
q029 factual=0, v(∅)=0.00, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.146
retrieve+0.125+0.125+0.208
answer+0.000+0.625+0.396
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 279; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.125
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.125
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 29'
'synthetic question 29'
difficulty
0.65
0.65
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q030 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.750+0.542
retrieve+0.125+0.375+0.271
answer+0.000+0.000+0.062
verify+0.000+0.125+0.125
◆

exact; 16 coalitions; cost 381; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.250
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 30'
'synthetic question 30'
difficulty
0.688
0.688
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q031 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.750+0.542
retrieve+0.000+0.000+0.021
answer+0.000+0.125+0.083
verify+0.000+0.375+0.229
◆

exact; 16 coalitions; cost 316; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.500
{verify}0.000
{rewrite, verify}0.750
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 31'
'synthetic question 31'
difficulty
0.389
0.389
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q032 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.750+0.479
retrieve+0.125+0.625+0.354
answer+0.000+0.125+0.042
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 290; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 32'
'synthetic question 32'
difficulty
0.135
0.135
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q033 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.198
retrieve+0.375+0.250+0.323
answer+0.250+0.125+0.219
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 274; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 33'
'synthetic question 33'
difficulty
0.721
0.721
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q034 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.625+0.604
retrieve+0.000+0.125+0.146
answer+0.125+0.000+0.188
verify+0.000+0.000+0.062
◆

exact; 16 coalitions; cost 359; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.000
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.875
{retrieve, answer}0.375
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.125
{rewrite, retrieve, verify}1.000
{answer, verify}0.125
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 34'
'synthetic question 34'
difficulty
0.525
0.525
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q036 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.271
retrieve+0.250+0.500+0.354
answer+0.375+0.125+0.292
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 308; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 36'
'synthetic question 36'
difficulty
0.486
0.486
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q037 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.229
retrieve+0.125+0.500+0.292
answer+0.000+0.500+0.229
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 310; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.250
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 37'
'synthetic question 37'
difficulty
0.889
0.889
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q038 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+1.000+0.500
retrieve+0.000+0.500+0.229
answer+0.000+0.125+0.104
verify+0.000+0.250+0.167
◆

exact; 16 coalitions; cost 381; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 38'
'synthetic question 38'
difficulty
0.934
0.934
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q039 factual=0, v(∅)=0.00, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.625+0.625+0.625
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 234; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 39'
'synthetic question 39'
difficulty
0.358
0.358
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q040 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.312
retrieve+0.500+0.250+0.438
answer+0.000+0.000+0.062
verify+0.000+0.000+0.062
◆

exact; 16 coalitions; cost 299; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 40'
'synthetic question 40'
difficulty
0.572
0.572
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q041 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.302
retrieve+0.250+0.375+0.302
answer+0.375+0.125+0.260
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 297; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 41'
'synthetic question 41'
difficulty
0.322
0.322
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q042 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.750+0.583
retrieve+0.000+0.000+0.000
answer+0.000+0.125+0.083
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 336; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 42'
'synthetic question 42'
difficulty
0.594
0.594
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q043 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.250+0.323
retrieve+0.625+0.500+0.531
answer+0.250+0.000+0.115
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 313; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.750
{rewrite, retrieve, verify}1.000
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 43'
'synthetic question 43'
difficulty
0.338
0.338
rewrite
'vague'
'vague'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q044 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.208
retrieve+0.625+0.750+0.729
answer+0.000+0.000+0.042
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 332; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.625
{rewrite, retrieve}0.875
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.750
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 44'
'synthetic question 44'
difficulty
0.392
0.392
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q045 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.750+0.375+0.562
verify+0.625+0.250+0.437
◆

exact; 16 coalitions; cost 216; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.750
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.625
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 45'
'synthetic question 45'
difficulty
0.89
0.89
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q046 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.208
retrieve+0.375+0.625+0.521
answer+0.000+0.125+0.104
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 322; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 46'
'synthetic question 46'
difficulty
0.227
0.227
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q047 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.208
retrieve+0.125+0.375+0.271
answer+0.000+0.500+0.271
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 276; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.250
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 47'
'synthetic question 47'
difficulty
0.623
0.623
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q048 factual=0, v(∅)=0.00, v(all)=0.38, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.271
retrieve+0.125+0.000+0.062
answer+0.000+0.000+0.021
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 308; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.375
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.375
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.375

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 48'
'synthetic question 48'
difficulty
0.084
0.084
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'irrelevant'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q050 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.625+0.500+0.542
retrieve+0.250+0.250+0.229
answer+0.000+0.125+0.062
verify+0.000+0.125+0.042
◆

exact; 16 coalitions; cost 338; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.625
{retrieve}0.250
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 50'
'synthetic question 50'
difficulty
0.787
0.787
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q052 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.625+0.375
retrieve+0.000+0.375+0.167
answer+0.125+0.250+0.188
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 280; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.500
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 52'
'synthetic question 52'
difficulty
0.876
0.876
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q053 factual=0, v(∅)=0.00, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.500+0.625+0.562
answer+0.000+0.000+0.000
verify+0.000+0.125+0.062
◆

exact; 16 coalitions; cost 241; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.500
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 53'
'synthetic question 53'
difficulty
0.059
0.059
rewrite
'precise'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'abstain'
q054 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.750+0.000+0.406
retrieve+0.875+0.125+0.531
answer+0.000+0.000+0.031
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 301; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.750
{retrieve}0.875
{rewrite, retrieve}0.875
{answer}0.000
{rewrite, answer}0.875
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.875
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.875
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 54'
'synthetic question 54'
difficulty
0.336
0.336
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q055 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.625+0.292
retrieve+0.000+0.625+0.292
answer+0.000+0.125+0.083
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 307; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.125
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.125
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 55'
'synthetic question 55'
difficulty
0.15
0.15
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'near_miss'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'abstain'
q056 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.625+0.500+0.542
retrieve+0.375+0.125+0.229
answer+0.000+0.250+0.104
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 318; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.625
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 56'
'synthetic question 56'
difficulty
0.45
0.45
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q057 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.750+0.604
retrieve+0.125+0.375+0.271
answer+0.000+0.000+0.062
verify+0.000+0.000+0.062
◆

exact; 16 coalitions; cost 350; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.125
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.250
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.250
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 57'
'synthetic question 57'
difficulty
0.796
0.796
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q058 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.625+0.417
retrieve+0.125+0.250+0.167
answer+0.000+0.375+0.167
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 310; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.375
{answer, verify}0.000
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 58'
'synthetic question 58'
difficulty
0.231
0.231
rewrite
'wrong_entity'
'wrong_entity'
retrieve
'irrelevant'
'irrelevant'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q059 factual=0, v(∅)=0.00, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.750+0.750+0.750
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 186; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.750
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.750
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 59'
'synthetic question 59'
difficulty
0.052
0.052
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q060 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.125+0.562
verify+0.875+0.000+0.437
◆

exact; 16 coalitions; cost 192; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.875
{rewrite, verify}0.875
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 60'
'synthetic question 60'
difficulty
0.405
0.405
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q061 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.375+0.688
verify+0.625+0.000+0.312
◆

exact; 16 coalitions; cost 192; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 61'
'synthetic question 61'
difficulty
0.199
0.199
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q062 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.625+0.875+0.771
answer+0.125+0.125+0.146
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 263; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.125
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.125
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 62'
'synthetic question 62'
difficulty
0.091
0.091
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q063 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.354
retrieve+0.250+0.000+0.229
answer+0.000+0.125+0.167
verify+0.000+0.125+0.125
◆

exact; 16 coalitions; cost 327; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 63'
'synthetic question 63'
difficulty
0.58
0.58
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'stale_fact'
verify
'stale_fact'
'correct'
q064 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.625+0.750+0.688
retrieve+0.125+0.250+0.188
answer+0.000+0.250+0.125
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 346; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.625
{retrieve}0.125
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.250
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 64'
'synthetic question 64'
difficulty
0.299
0.299
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q066 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.875+0.125+0.500
verify+0.875+0.125+0.500
◆

exact; 16 coalitions; cost 189; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.875
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.875
{rewrite, verify}0.875
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 66'
'synthetic question 66'
difficulty
0.2
0.2
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q067 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.875+0.667
retrieve+0.125+0.250+0.188
answer+0.000+0.000+0.042
verify+0.000+0.125+0.104
◆

exact; 16 coalitions; cost 347; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.125
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.750
{retrieve, verify}0.125
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 67'
'synthetic question 67'
difficulty
0.942
0.942
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q068 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.375+0.750+0.625
answer+0.125+0.125+0.187
verify+0.000+0.000+0.062
◆

exact; 16 coalitions; cost 255; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.375
{rewrite, retrieve}0.375
{answer}0.125
{rewrite, answer}0.125
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.125
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 68'
'synthetic question 68'
difficulty
0.365
0.365
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q069 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.500+0.281
retrieve+0.125+0.625+0.406
answer+0.250+0.125+0.260
verify+0.000+0.000+0.052
◆

exact; 16 coalitions; cost 317; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.125
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 69'
'synthetic question 69'
difficulty
0.105
0.105
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q070 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.750+0.667
retrieve+0.125+0.125+0.146
answer+0.000+0.000+0.042
verify+0.000+0.250+0.146
◆

exact; 16 coalitions; cost 364; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.125
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.875
{retrieve, verify}0.125
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 70'
'synthetic question 70'
difficulty
0.629
0.629
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q071 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.333
retrieve+0.125+0.500+0.333
answer+0.125+0.125+0.125
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 322; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.250
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 71'
'synthetic question 71'
difficulty
0.927
0.927
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q072 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.750+0.365
retrieve+0.000+0.625+0.281
answer+0.000+0.125+0.073
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 309; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.125
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.125
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 72'
'synthetic question 72'
difficulty
0.44
0.44
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q073 factual=0, v(∅)=0.00, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.625+0.365
retrieve+0.000+0.375+0.177
answer+0.000+0.000+0.010
verify+0.000+0.125+0.073
◆

exact; 16 coalitions; cost 324; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.125
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.500
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 73'
'synthetic question 73'
difficulty
0.955
0.955
rewrite
'wrong_entity'
'wrong_entity'
retrieve
'irrelevant'
'near_miss'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'abstain'
q074 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.250
retrieve+0.750+0.500+0.625
◆
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 317; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.750
{rewrite, retrieve}0.875
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 74'
'synthetic question 74'
difficulty
0.5
0.5
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q075 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.500+0.344
retrieve+0.250+0.625+0.406
answer+0.125+0.125+0.115
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 322; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.250
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 75'
'synthetic question 75'
difficulty
0.425
0.425
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q077 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.000+0.104
retrieve+0.500+0.750+0.646
answer+0.125+0.125+0.146
verify+0.000+0.125+0.104
◆

exact; 16 coalitions; cost 307; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.250
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.250
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 77'
'synthetic question 77'
difficulty
0.995
0.995
rewrite
'vague'
'vague'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q078 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.125
retrieve+0.500+0.625+0.667
answer+0.000+0.000+0.104
verify+0.000+0.000+0.104
◆

exact; 16 coalitions; cost 322; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 78'
'synthetic question 78'
difficulty
0.949
0.949
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q079 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.365
retrieve+0.375+0.250+0.365
answer+0.250+0.125+0.240
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 314; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 79'
'synthetic question 79'
difficulty
0.46
0.46
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q083 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.875+0.490
retrieve+0.000+0.625+0.302
answer+0.000+0.375+0.198
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 347; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.125
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 83'
'synthetic question 83'
difficulty
0.786
0.786
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q086 factual=0, v(∅)=0.00, v(all)=0.50, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.292
retrieve+0.000+0.250+0.104
answer+0.000+0.250+0.104
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 260; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.500
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.250
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.500

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 86'
'synthetic question 86'
difficulty
0.711
0.711
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q089 factual=0, v(∅)=0.00, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.292
retrieve+0.375+0.250+0.292
answer+0.000+0.125+0.042
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 285; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.500
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 89'
'synthetic question 89'
difficulty
0.729
0.729
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q090 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.875+0.250+0.562
verify+0.750+0.125+0.438
◆

exact; 16 coalitions; cost 237; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.875
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.750
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 90'
'synthetic question 90'
difficulty
0.927
0.927
rewrite
'wrong_entity'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q091 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.500+0.385
retrieve+0.250+0.625+0.448
answer+0.000+0.000+0.073
verify+0.000+0.125+0.094
◆

exact; 16 coalitions; cost 333; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 91'
'synthetic question 91'
difficulty
0.968
0.968
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q093 factual=0, v(∅)=0.00, v(all)=0.62, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.250
retrieve+0.000+0.125+0.104
answer+0.375+0.000+0.250
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 298; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 93'
'synthetic question 93'
difficulty
0.864
0.864
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q094 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.875+0.490
retrieve+0.000+0.500+0.219
answer+0.125+0.125+0.198
verify+0.000+0.125+0.094
◆

exact; 16 coalitions; cost 331; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.125
{rewrite, answer}0.500
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 94'
'synthetic question 94'
difficulty
0.981
0.981
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q095 factual=0, v(∅)=0.00, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.000+0.260
retrieve+0.250+0.000+0.260
answer+0.000+0.250+0.260
verify+0.000+0.000+0.094
◆

exact; 16 coalitions; cost 326; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 95'
'synthetic question 95'
difficulty
0.957
0.957
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q096 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.292
retrieve+0.250+0.375+0.417
answer+0.000+0.250+0.229
verify+0.000+0.000+0.062
◆

exact; 16 coalitions; cost 345; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 96'
'synthetic question 96'
difficulty
0.149
0.149
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q098 factual=0, v(∅)=0.00, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.750+0.750+0.750
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 186; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.750
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.750
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 98'
'synthetic question 98'
difficulty
0.89
0.89
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q099 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.750+0.646
retrieve+0.000+0.125+0.062
answer+0.000+0.000+0.021
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 293; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.000
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 99'
'synthetic question 99'
difficulty
0.822
0.822
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q100 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.625+0.750+0.688
answer+0.000+0.125+0.062
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 237; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 100'
'synthetic question 100'
difficulty
0.48
0.48
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q101 factual=0, v(∅)=0.00, v(all)=0.62, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.625+0.625+0.625
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 183; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.625
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.625
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 101'
'synthetic question 101'
difficulty
0.232
0.232
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q102 factual=0, v(∅)=0.00, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.500+0.312
answer+0.125+0.250+0.250
verify+0.000+0.000+0.062
◆

exact; 16 coalitions; cost 242; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.125
{rewrite, answer}0.125
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.375
{answer, verify}0.125
{rewrite, answer, verify}0.125
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 102'
'synthetic question 102'
difficulty
0.802
0.802
rewrite
'precise'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q103 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.062
retrieve+0.250+0.875+0.646
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 275; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 103'
'synthetic question 103'
difficulty
0.924
0.924
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q104 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.750+0.875+0.833
answer+0.000+0.000+0.021
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 254; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 104'
'synthetic question 104'
difficulty
0.266
0.266
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q105 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.875+0.250+0.562
verify+0.750+0.125+0.438
◆

exact; 16 coalitions; cost 225; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.875
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.750
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 105'
'synthetic question 105'
difficulty
0.539
0.539
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q107 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.875+0.750+0.812
retrieve+0.250+0.000+0.125
answer+0.000+0.125+0.062
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 332; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.875
{retrieve}0.250
{rewrite, retrieve}0.875
{answer}0.000
{rewrite, answer}1.000
{retrieve, answer}0.250
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.875
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 107'
'synthetic question 107'
difficulty
0.931
0.931
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q108 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.750+0.635
retrieve+0.125+0.250+0.156
answer+0.125+0.000+0.115
verify+0.000+0.125+0.094
◆

exact; 16 coalitions; cost 381; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.125
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.750
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.750
{retrieve, verify}0.125
{rewrite, retrieve, verify}1.000
{answer, verify}0.125
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 108'
'synthetic question 108'
difficulty
0.041
0.041
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q109 factual=0, v(∅)=0.00, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.875+0.875+0.875
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 189; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.875
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.875
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 109'
'synthetic question 109'
difficulty
0.732
0.732
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q110 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.292
retrieve+0.125+0.375+0.292
answer+0.000+0.125+0.125
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 322; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 110'
'synthetic question 110'
difficulty
0.614
0.614
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q111 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.875+0.708
retrieve+0.000+0.250+0.146
answer+0.000+0.125+0.083
verify+0.000+0.125+0.062
◆

exact; 16 coalitions; cost 350; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.000
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 111'
'synthetic question 111'
difficulty
0.028
0.028
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q113 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.250+0.396
retrieve+0.500+0.250+0.396
answer+0.250+0.125+0.208
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 328; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.875
{answer}0.250
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 113'
'synthetic question 113'
difficulty
0.016
0.016
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q115 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.625+0.333
retrieve+0.125+0.625+0.333
answer+0.250+0.000+0.146
verify+0.000+0.125+0.062
◆

exact; 16 coalitions; cost 317; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.250
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 115'
'synthetic question 115'
difficulty
0.513
0.513
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q116 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.625+0.312
retrieve+0.000+0.625+0.312
answer+0.000+0.250+0.167
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 311; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 116'
'synthetic question 116'
difficulty
0.929
0.929
rewrite
'vague'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'stale_fact'
'abstain'
verify
'stale_fact'
'abstain'
q117 factual=0, v(∅)=0.00, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.625+0.479
retrieve+0.000+0.125+0.042
answer+0.000+0.250+0.104
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 265; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.375
{answer, verify}0.000
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 117'
'synthetic question 117'
difficulty
0.066
0.066
rewrite
'wrong_entity'
'wrong_entity'
retrieve
'near_miss'
'near_miss'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q118 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.281
retrieve+0.375+0.375+0.406
answer+0.125+0.125+0.156
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 302; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 118'
'synthetic question 118'
difficulty
0.841
0.841
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q120 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.250+0.365
retrieve+0.500+0.250+0.365
answer+0.125+0.125+0.115
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 333; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 120'
'synthetic question 120'
difficulty
0.344
0.344
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q121 factual=0, v(∅)=0.00, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.125+0.625+0.375
answer+0.000+0.500+0.250
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 246; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.125
{rewrite, retrieve}0.125
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.125
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 121'
'synthetic question 121'
difficulty
0.43
0.43
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q122 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.500+0.250
retrieve+0.000+0.625+0.312
answer+0.125+0.000+0.104
verify+0.000+0.375+0.208
◆

exact; 16 coalitions; cost 293; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.125
{rewrite, answer}0.125
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.500
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 122'
'synthetic question 122'
difficulty
0.966
0.966
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q123 factual=0, v(∅)=0.00, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.250+0.625+0.438
answer+0.000+0.375+0.188
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 232; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.250
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 123'
'synthetic question 123'
difficulty
0.562
0.562
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q124 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.750+1.000+0.917
answer+0.000+0.000+0.042
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 271; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 124'
'synthetic question 124'
difficulty
0.259
0.259
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q126 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.500+0.750+0.646
answer+0.000+0.000+0.021
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 252; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 126'
'synthetic question 126'
difficulty
0.888
0.888
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q127 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.281
retrieve+0.500+0.375+0.469
answer+0.250+0.125+0.240
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 307; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 127'
'synthetic question 127'
difficulty
0.226
0.226
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q128 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.625+0.427
retrieve+0.250+0.625+0.427
answer+0.125+0.125+0.135
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 331; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.750
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 128'
'synthetic question 128'
difficulty
0.125
0.125
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q129 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.875+0.594
retrieve+0.000+0.250+0.156
answer+0.000+0.000+0.094
verify+0.000+0.125+0.156
◆

exact; 16 coalitions; cost 327; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.750
{retrieve, verify}0.125
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 129'
'synthetic question 129'
difficulty
0.288
0.288
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q130 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.250+0.385
retrieve+0.500+0.250+0.385
answer+0.000+0.125+0.073
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 343; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 130'
'synthetic question 130'
difficulty
0.586
0.586
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q131 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.323
retrieve+0.375+0.250+0.323
answer+0.375+0.000+0.219
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 317; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 131'
'synthetic question 131'
difficulty
0.554
0.554
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q132 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.750+1.000+0.896
answer+0.000+0.125+0.083
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 274; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 132'
'synthetic question 132'
difficulty
0.81
0.81
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q133 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.625+0.479
retrieve+0.125+0.375+0.292
answer+0.000+0.000+0.062
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 375; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 133'
'synthetic question 133'
difficulty
0.56
0.56
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q135 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.875+0.125+0.500
verify+0.875+0.125+0.500
◆

exact; 16 coalitions; cost 189; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.875
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.875
{rewrite, verify}0.875
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 135'
'synthetic question 135'
difficulty
0.413
0.413
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q136 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.750+0.490
retrieve+0.125+0.375+0.260
answer+0.000+0.000+0.094
verify+0.000+0.125+0.156
◆

exact; 16 coalitions; cost 384; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.250
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 136'
'synthetic question 136'
difficulty
0.818
0.818
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q137 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.219
retrieve+0.125+0.500+0.385
answer+0.000+0.250+0.198
verify+0.000+0.000+0.073
◆

exact; 16 coalitions; cost 313; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 137'
'synthetic question 137'
difficulty
0.627
0.627
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q140 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.229
retrieve+0.375+0.500+0.479
answer+0.000+0.250+0.167
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 312; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 140'
'synthetic question 140'
difficulty
0.553
0.553
rewrite
'vague'
'vague'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q142 factual=0, v(∅)=0.00, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.500+0.625+0.562
answer+0.000+0.125+0.062
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 237; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.500
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 142'
'synthetic question 142'
difficulty
0.848
0.848
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q143 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.500+0.875+0.729
answer+0.000+0.125+0.104
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 277; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 143'
'synthetic question 143'
difficulty
0.145
0.145
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q145 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.250+0.625
verify+0.750+0.000+0.375
◆

exact; 16 coalitions; cost 192; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.750
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 145'
'synthetic question 145'
difficulty
0.91
0.91
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q146 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.875+0.000+0.448
retrieve+0.875+0.000+0.448
answer+0.125+0.000+0.073
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 328; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.875
{retrieve}0.875
{rewrite, retrieve}0.875
{answer}0.125
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}1.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.125
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 146'
'synthetic question 146'
difficulty
0.043
0.043
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q148 factual=0, v(∅)=0.00, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.250
retrieve+0.250+0.250+0.250
answer+0.125+0.000+0.104
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 286; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 148'
'synthetic question 148'
difficulty
0.415
0.415
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q150 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.625+0.500+0.583
retrieve+0.250+0.000+0.125
answer+0.000+0.000+0.021
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 308; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.625
{retrieve}0.250
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.750
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 150'
'synthetic question 150'
difficulty
0.01
0.01
rewrite
'wrong_entity'
'wrong_entity'
retrieve
'irrelevant'
'irrelevant'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q151 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.146
retrieve+0.500+0.625+0.604
answer+0.000+0.125+0.104
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 310; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 151'
'synthetic question 151'
difficulty
0.365
0.365
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q153 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.250+0.625
verify+0.750+0.000+0.375
◆

exact; 16 coalitions; cost 222; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.750
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 153'
'synthetic question 153'
difficulty
0.653
0.653
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q155 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.875+0.625
retrieve+0.000+0.125+0.042
answer+0.000+0.375+0.188
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 350; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.500
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 155'
'synthetic question 155'
difficulty
0.703
0.703
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q156 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.156
retrieve+0.125+0.375+0.302
answer+0.250+0.000+0.219
verify+0.000+0.000+0.073
◆

exact; 16 coalitions; cost 302; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.250
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.250
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 156'
'synthetic question 156'
difficulty
0.944
0.944
rewrite
'vague'
'vague'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'abstain'
q158 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.750+0.875+0.854
answer+0.125+0.000+0.104
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 274; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.125
{rewrite, answer}0.125
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.125
{rewrite, answer, verify}0.125
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 158'
'synthetic question 158'
difficulty
0.865
0.865
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q159 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.271
retrieve+0.500+0.250+0.333
answer+0.625+0.125+0.375
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 328; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 159'
'synthetic question 159'
difficulty
0.059
0.059
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q162 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.250+0.375
retrieve+0.625+0.375+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 302; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.875
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 162'
'synthetic question 162'
difficulty
0.489
0.489
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q163 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.625+0.750+0.667
retrieve+0.125+0.250+0.167
answer+0.000+0.125+0.042
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 365; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.625
{retrieve}0.125
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 163'
'synthetic question 163'
difficulty
0.976
0.976
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q165 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.750+0.677
retrieve+0.000+0.125+0.094
answer+0.000+0.000+0.052
verify+0.000+0.000+0.052
◆

exact; 16 coalitions; cost 325; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.500
{retrieve}0.000
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.750
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 165'
'synthetic question 165'
difficulty
0.309
0.309
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q166 factual=0, v(∅)=0.00, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.271
retrieve+0.375+0.125+0.271
answer+0.000+0.125+0.083
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 283; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.500
{answer, verify}0.000
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 166'
'synthetic question 166'
difficulty
0.27
0.27
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q167 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.625+0.573
retrieve+0.125+0.125+0.156
answer+0.000+0.000+0.052
verify+0.000+0.250+0.219
◆

exact; 16 coalitions; cost 384; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.125
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.875
{retrieve, verify}0.375
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 167'
'synthetic question 167'
difficulty
0.863
0.863
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q169 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.625+1.000+0.812
answer+0.000+0.375+0.188
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 265; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 169'
'synthetic question 169'
difficulty
0.511
0.511
rewrite
'precise'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q170 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.250+0.875+0.625
answer+0.000+0.125+0.125
verify+0.000+0.125+0.125
◆

exact; 16 coalitions; cost 263; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 170'
'synthetic question 170'
difficulty
0.344
0.344
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q171 factual=0, v(∅)=0.00, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+1.000+0.250+0.625
verify+0.750+0.000+0.375
◆

exact; 16 coalitions; cost 234; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}1.000
{rewrite, answer}1.000
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.750
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}1.000
{rewrite, answer, verify}1.000
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 171'
'synthetic question 171'
difficulty
0.995
0.995
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q172 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.750+0.500
◆
retrieve+0.125+0.500+0.312
answer+0.000+0.125+0.062
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 296; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.750
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 172'
'synthetic question 172'
difficulty
0.316
0.316
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q173 factual=0, v(∅)=0.00, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.750+0.750+0.750
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 234; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.750
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.750
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 173'
'synthetic question 173'
difficulty
0.183
0.183
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q174 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.250+0.875+0.646
answer+0.000+0.000+0.083
verify+0.000+0.125+0.146
◆

exact; 16 coalitions; cost 283; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 174'
'synthetic question 174'
difficulty
0.88
0.88
rewrite
'precise'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q175 factual=0, v(∅)=0.00, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.125
retrieve+0.125+0.500+0.312
◆
answer+0.000+0.375+0.188
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 306; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.125
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.250
{answer, verify}0.000
{rewrite, answer, verify}0.125
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 175'
'synthetic question 175'
difficulty
0.812
0.812
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q176 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.750+0.396
retrieve+0.000+0.625+0.312
answer+0.000+0.000+0.083
verify+0.000+0.000+0.083
◆

exact; 16 coalitions; cost 347; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.250
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 176'
'synthetic question 176'
difficulty
0.668
0.668
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q177 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.750+0.531
retrieve+0.000+0.250+0.156
answer+0.000+0.000+0.094
verify+0.000+0.000+0.094
◆

exact; 16 coalitions; cost 395; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.125
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.125
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 177'
'synthetic question 177'
difficulty
0.958
0.958
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q178 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.156
retrieve+0.000+0.625+0.365
answer+0.000+0.125+0.115
verify+0.000+0.125+0.115
◆

exact; 16 coalitions; cost 279; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.125
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.125
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 178'
'synthetic question 178'
difficulty
0.926
0.926
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q179 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.271
retrieve+0.375+0.375+0.396
answer+0.000+0.125+0.083
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 302; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 179'
'synthetic question 179'
difficulty
0.748
0.748
rewrite
'vague'
'precise'
retrieve
'stale'
'stale'
answer
'stale_fact'
'abstain'
verify
'stale_fact'
'abstain'
q181 factual=0, v(∅)=0.00, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.625+0.625+0.625
answer+0.125+0.125+0.125
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 235; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.125
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.125
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 181'
'synthetic question 181'
difficulty
0.247
0.247
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q182 factual=0, v(∅)=0.00, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.750+0.750+0.750
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 186; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.750
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.750
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 182'
'synthetic question 182'
difficulty
0.141
0.141
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q183 factual=0, v(∅)=0.00, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.625+0.396
retrieve+0.000+0.625+0.333
answer+0.125+0.125+0.146
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 321; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.000
{rewrite, retrieve}0.750
{answer}0.125
{rewrite, answer}0.250
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.125
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 183'
'synthetic question 183'
difficulty
0.67
0.67
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q184 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.385
retrieve+0.250+0.375+0.385
answer+0.000+0.125+0.156
verify+0.000+0.000+0.073
◆

exact; 16 coalitions; cost 331; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 184'
'synthetic question 184'
difficulty
0.715
0.715
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q185 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.625+0.750+0.688
retrieve+0.250+0.375+0.312
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 332; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.625
{retrieve}0.250
{rewrite, retrieve}1.000
{answer}0.000
{rewrite, answer}0.625
{retrieve, answer}0.250
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.250
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 185'
'synthetic question 185'
difficulty
0.167
0.167
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q187 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.750+0.458
retrieve+0.000+0.375+0.229
answer+0.000+0.125+0.167
verify+0.000+0.125+0.146
◆

exact; 16 coalitions; cost 389; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.250
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.875
{answer, verify}0.000
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 187'
'synthetic question 187'
difficulty
0.91
0.91
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q188 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.750+0.583
retrieve+0.000+0.125+0.104
answer+0.000+0.250+0.208
verify+0.000+0.125+0.104
◆

exact; 16 coalitions; cost 395; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.750
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.625
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.250
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 188'
'synthetic question 188'
difficulty
0.561
0.561
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q191 factual=0, v(∅)=0.00, v(all)=0.62, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.625+0.625+0.625
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 183; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.000
{answer}0.625
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.000
{answer, verify}0.625
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 191'
'synthetic question 191'
difficulty
0.526
0.526
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q192 factual=0, v(∅)=0.00, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.000+0.146
retrieve+0.375+0.500+0.458
answer+0.000+0.500+0.271
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 298; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.375
{answer, verify}0.000
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 192'
'synthetic question 192'
difficulty
0.523
0.523
rewrite
'vague'
'vague'
retrieve
'stale'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'

… 4 more cases omitted.

Interventional blame (fresh noise)

200 cases run, 154 failures, 154 analyzed, 0 not fixable by any combination of fixes. Cost 40962. all failures analyzed.

{'mode': 'prior', 'n_worlds': 8, 'crn': True, 'method': 'auto', 'ci': 'normal', 'delta': 0.05}

stepfixing this step alone resolvesmean Shapley blame (±CI)sharelast-touch
retrieve20.5%
+0.244
38.7%7
rewrite17.3%
+0.202
32.0%8
answer11.4%
+0.130
20.5%0
verify5.6%
+0.056
8.8%103
Per-case drill-down
q000 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.625+0.396
retrieve+0.125+0.250+0.208
answer+0.125+0.250+0.292
verify+0.000+0.000+0.104
◆

exact; 16 coalitions; cost 322; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.125
{rewrite, retrieve}0.125
{answer}0.125
{rewrite, answer}0.750
{retrieve, answer}0.375
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.500
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 0'
'synthetic question 0'
difficulty
0.637
0.637
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q001 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.083
retrieve+0.375+0.375+0.396
answer+0.125+0.125+0.146
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 250; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.375
{retrieve}0.750
{rewrite, retrieve}0.875
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.375
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 1'
'synthetic question 1'
difficulty
0.27
0.27
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q004 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.271
retrieve+0.375+0.500+0.458
answer+0.000+0.000+0.042
verify+0.000+0.125+0.104
◆

exact; 16 coalitions; cost 281; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.500
{retrieve, verify}0.750
{rewrite, retrieve, verify}1.000
{answer, verify}0.125
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 4'
'synthetic question 4'
difficulty
0.813
0.813
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q005 factual=0, v(∅)=0.38, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.177
retrieve+0.000+0.125+0.052
answer+0.125+0.000+0.073
verify+0.125+0.000+0.073
◆

exact; 16 coalitions; cost 229; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 5'
'synthetic question 5'
difficulty
0.913
0.913
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q006 factual=0, v(∅)=0.50, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.208
retrieve+0.000+0.250+0.146
answer+0.000+0.000+0.021
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 264; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.500
{rewrite, retrieve}0.875
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 6'
'synthetic question 6'
difficulty
0.607
0.607
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q007 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.302
retrieve+0.375+0.500+0.406
answer+0.125+0.000+0.115
verify+0.000+0.000+0.052
◆

exact; 16 coalitions; cost 341; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.500
{rewrite, retrieve, answer}1.000
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}1.000
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 7'
'synthetic question 7'
difficulty
0.729
0.729
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q008 factual=0, v(∅)=0.62, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.083
retrieve+0.125+0.125+0.146
answer+0.125+0.125+0.146
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 236; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.875
{answer}0.750
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.750
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 8'
'synthetic question 8'
difficulty
0.544
0.544
rewrite
'vague'
'vague'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q009 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.156
retrieve+0.125+0.375+0.281
answer+0.250+0.125+0.219
verify+0.125+0.000+0.094
◆

exact; 16 coalitions; cost 268; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.125
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 9'
'synthetic question 9'
difficulty
0.935
0.935
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q010 factual=0, v(∅)=0.12, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.375+0.375
retrieve+0.250+0.125+0.188
answer+0.000+0.250+0.125
verify+0.000+0.125+0.062
◆

exact; 16 coalitions; cost 279; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.625
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.625
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 10'
'synthetic question 10'
difficulty
0.816
0.816
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q011 factual=0, v(∅)=0.50, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.083
◆
retrieve+0.125+0.250+0.208
answer+0.125+0.250+0.208
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 251; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 11'
'synthetic question 11'
difficulty
0.003
0.003
rewrite
'vague'
'precise'
retrieve
'stale'
'near_miss'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q012 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.000+0.208
retrieve+0.625+0.250+0.458
answer+0.375+0.250+0.333
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 296; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 12'
'synthetic question 12'
difficulty
0.857
0.857
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q013 factual=0, v(∅)=0.38, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.000+0.125
retrieve+0.250+0.000+0.125
answer+0.125+0.000+0.062
verify+0.125+0.000+0.062
◆

exact; 16 coalitions; cost 208; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.500
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.500
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.500
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 13'
'synthetic question 13'
difficulty
0.034
0.034
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q014 factual=0, v(∅)=0.25, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.312
retrieve+0.500+0.125+0.354
answer+0.000+0.000+0.062
verify+0.000+0.000+0.021

exact; 16 coalitions; cost 304; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.875
{answer}0.250
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.250
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}1.000
{answer, verify}0.250
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 14'
'synthetic question 14'
difficulty
0.73
0.73
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q015 factual=0, v(∅)=0.25, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.312
retrieve+0.250+0.250+0.271
answer+0.000+0.000+0.021
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 273; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.625
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 15'
'synthetic question 15'
difficulty
0.176
0.176
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q016 factual=0, v(∅)=0.12, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.229
retrieve+0.250+0.250+0.229
◆
answer+0.000+0.000+0.000
verify+0.000+0.125+0.042

exact; 16 coalitions; cost 259; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.500
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 16'
'synthetic question 16'
difficulty
0.863
0.863
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'abstain'
verify
'stale_fact'
'abstain'
q017 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.312
retrieve+0.375+0.500+0.500
answer+0.000+0.000+0.083
verify+0.000+0.125+0.104
◆

exact; 16 coalitions; cost 327; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.000
{rewrite, answer}0.375
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}1.000
{answer, verify}0.000
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 17'
'synthetic question 17'
difficulty
0.541
0.541
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q018 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.083
retrieve+0.125+0.375+0.271
answer+0.125+0.125+0.167
verify+0.125+0.000+0.104
◆

exact; 16 coalitions; cost 264; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.375
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 18'
'synthetic question 18'
difficulty
0.3
0.3
rewrite
'vague'
'vague'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q019 factual=0, v(∅)=0.12, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.250
retrieve+0.250+0.125+0.188
answer+0.250+0.125+0.187
verify+0.250+0.000+0.125
◆

exact; 16 coalitions; cost 274; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 19'
'synthetic question 19'
difficulty
0.423
0.423
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q022 factual=0, v(∅)=0.62, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.031
retrieve+0.125+0.250+0.219
answer+0.000+0.125+0.094
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 222; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.750
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 22'
'synthetic question 22'
difficulty
0.671
0.671
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q023 factual=0, v(∅)=0.12, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.333
retrieve+0.000+0.000+0.000
answer+0.250+0.000+0.146
verify+0.250+0.000+0.146
◆

exact; 16 coalitions; cost 257; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.125
{rewrite, retrieve}0.375
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 23'
'synthetic question 23'
difficulty
0.647
0.647
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q025 factual=0, v(∅)=0.62, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.062
retrieve+0.000+0.000+0.000
answer+0.250+0.375+0.312
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 206; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.875
{rewrite, answer}1.000
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.875
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 25'
'synthetic question 25'
difficulty
0.384
0.384
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q026 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.271
retrieve+0.125+0.500+0.333
answer+0.000+0.125+0.125
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 296; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 26'
'synthetic question 26'
difficulty
0.997
0.997
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q027 factual=0, v(∅)=0.38, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.083
retrieve+0.000+0.125+0.083
◆
answer+0.125+0.000+0.083
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 234; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.500
{rewrite, answer}0.500
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.625
{verify}0.375
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.500
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 27'
'synthetic question 27'
difficulty
0.981
0.981
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q029 factual=0, v(∅)=0.25, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.250+0.250+0.250
answer+0.125+0.125+0.125
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 234; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.250
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 29'
'synthetic question 29'
difficulty
0.65
0.65
rewrite
'vague'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q030 factual=0, v(∅)=0.38, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.177
retrieve+0.250+0.375+0.302
answer+0.000+0.000+0.010
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 262; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 30'
'synthetic question 30'
difficulty
0.688
0.688
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q031 factual=0, v(∅)=0.12, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.500+0.396
retrieve+0.375+0.500+0.396
answer+0.000+0.125+0.042
verify+0.000+0.125+0.042
◆

exact; 16 coalitions; cost 315; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.125
{rewrite, answer}0.500
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 31'
'synthetic question 31'
difficulty
0.389
0.389
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'stale_fact'
verify
'hallucinated'
'correct'
q032 factual=0, v(∅)=0.38, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.062
retrieve+0.250+0.125+0.188
answer+0.250+0.000+0.125
verify+0.250+0.000+0.125

exact; 16 coalitions; cost 202; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.625
{rewrite, verify}0.750
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 32'
'synthetic question 32'
difficulty
0.135
0.135
rewrite
'wrong_entity'
'vague'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q033 factual=0, v(∅)=0.12, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.333
retrieve+0.125+0.375+0.271
answer+0.250+0.250+0.271
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 293; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.500
{rewrite, retrieve, answer}1.000
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 33'
'synthetic question 33'
difficulty
0.721
0.721
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q034 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.156
retrieve+0.250+0.375+0.344
answer+0.250+0.250+0.281
verify+0.125+0.000+0.094
◆

exact; 16 coalitions; cost 285; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 34'
'synthetic question 34'
difficulty
0.525
0.525
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q036 factual=0, v(∅)=0.38, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.125+0.250+0.208
answer+0.125+0.125+0.146
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 242; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 36'
'synthetic question 36'
difficulty
0.486
0.486
rewrite
'vague'
'vague'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q037 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.000+0.208
retrieve+0.500+0.125+0.333
answer+0.125+0.125+0.125
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 276; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.250
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 37'
'synthetic question 37'
difficulty
0.889
0.889
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q038 factual=0, v(∅)=0.12, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.292
retrieve+0.000+0.375+0.146
answer+0.125+0.375+0.250
verify+0.000+0.125+0.062
◆

exact; 16 coalitions; cost 293; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.500
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 38'
'synthetic question 38'
difficulty
0.934
0.934
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q039 factual=0, v(∅)=0.12, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.125+0.125+0.125
answer+0.250+0.000+0.125
verify+0.125+0.125+0.125
◆

exact; 16 coalitions; cost 243; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.375
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.500
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 39'
'synthetic question 39'
difficulty
0.358
0.358
rewrite
'precise'
'precise'
retrieve
'near_miss'
'irrelevant'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q040 factual=0, v(∅)=0.12, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.292
retrieve+0.250+0.250+0.250
answer+0.375+0.250+0.312
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 265; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.500
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.125
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.500
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 40'
'synthetic question 40'
difficulty
0.572
0.572
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q041 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.375+0.156
retrieve+0.250+0.750+0.490
answer+0.125+0.125+0.135
verify+0.125+0.000+0.094
◆

exact; 16 coalitions; cost 313; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.125
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.250
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.250
{rewrite, verify}0.250
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 41'
'synthetic question 41'
difficulty
0.322
0.322
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q042 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.229
retrieve+0.375+0.500+0.438
answer+0.125+0.000+0.083
verify+0.125+0.125+0.125
◆

exact; 16 coalitions; cost 258; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.750
{rewrite, retrieve, verify}1.000
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 42'
'synthetic question 42'
difficulty
0.594
0.594
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q043 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.146
retrieve+0.125+0.375+0.271
answer+0.125+0.125+0.146
verify+0.125+0.000+0.062
◆

exact; 16 coalitions; cost 251; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 43'
'synthetic question 43'
difficulty
0.338
0.338
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q044 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.156
◆
retrieve+0.250+0.500+0.406
answer+0.000+0.000+0.031
verify+0.000+0.000+0.031

exact; 16 coalitions; cost 273; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.250
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.375
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.375
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 44'
'synthetic question 44'
difficulty
0.392
0.392
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q045 factual=0, v(∅)=0.25, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.000+0.188
retrieve+0.375+0.000+0.188
◆
answer+0.125+0.125+0.125
verify+0.125+0.125+0.125

exact; 16 coalitions; cost 263; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.500
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 45'
'synthetic question 45'
difficulty
0.89
0.89
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q046 factual=0, v(∅)=0.50, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.083
retrieve+0.250+0.125+0.188
answer+0.250+0.000+0.146
verify+0.125+0.000+0.083

exact; 16 coalitions; cost 225; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.500
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.750
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.750
{retrieve, verify}0.875
{rewrite, retrieve, verify}1.000
{answer, verify}0.750
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 46'
'synthetic question 46'
difficulty
0.227
0.227
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q047 factual=0, v(∅)=0.12, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.000+0.250+0.146
answer+0.250+0.125+0.208
verify+0.250+0.000+0.146
◆

exact; 16 coalitions; cost 242; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 47'
'synthetic question 47'
difficulty
0.623
0.623
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q048 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.167
retrieve+0.375+0.250+0.292
answer+0.125+0.250+0.167
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 253; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 48'
'synthetic question 48'
difficulty
0.084
0.084
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q050 factual=0, v(∅)=0.12, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.177
retrieve+0.250+0.500+0.365
answer+0.000+0.125+0.073
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 258; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.250
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 50'
'synthetic question 50'
difficulty
0.787
0.787
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q052 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.281
retrieve+0.125+0.500+0.365
answer+0.000+0.250+0.177
verify+0.000+0.000+0.052
◆

exact; 16 coalitions; cost 326; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 52'
'synthetic question 52'
difficulty
0.876
0.876
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q053 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.500+0.500+0.500
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 258; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.875
{rewrite, retrieve}1.000
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.875
{rewrite, retrieve, verify}1.000
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 53'
'synthetic question 53'
difficulty
0.059
0.059
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q054 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.177
retrieve+0.375+0.500+0.427
answer+0.000+0.000+0.010
verify+0.000+0.000+0.010

exact; 16 coalitions; cost 267; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.750
{rewrite, retrieve}0.875
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.750
{rewrite, retrieve, verify}1.000
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 54'
'synthetic question 54'
difficulty
0.336
0.336
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q055 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.250
retrieve+0.250+0.500+0.375
answer+0.000+0.250+0.125
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 307; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 55'
'synthetic question 55'
difficulty
0.15
0.15
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q056 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.083
retrieve+0.250+0.250+0.292
answer+0.250+0.000+0.167
verify+0.125+0.000+0.083
◆

exact; 16 coalitions; cost 259; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.875
{rewrite, retrieve, verify}1.000
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 56'
'synthetic question 56'
difficulty
0.45
0.45
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q057 factual=0, v(∅)=0.12, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.250+0.396
retrieve+0.375+0.125+0.271
answer+0.000+0.000+0.042
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 290; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.625
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.750
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.750
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 57'
'synthetic question 57'
difficulty
0.796
0.796
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q058 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.250+0.375+0.312
answer+0.125+0.250+0.188
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 256; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 58'
'synthetic question 58'
difficulty
0.231
0.231
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q059 factual=0, v(∅)=0.38, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.083
retrieve+0.125+0.250+0.208
answer+0.375+0.125+0.271
verify+0.125+0.000+0.062

exact; 16 coalitions; cost 236; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.750
{rewrite, answer}0.750
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.750
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 59'
'synthetic question 59'
difficulty
0.052
0.052
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q060 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.000+0.125
retrieve+0.375+0.125+0.250
answer+0.250+0.000+0.125
verify+0.250+0.000+0.125
◆

exact; 16 coalitions; cost 234; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.625
{rewrite, answer}0.875
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.875
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.625
{rewrite, answer, verify}0.875
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 60'
'synthetic question 60'
difficulty
0.405
0.405
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q061 factual=0, v(∅)=0.50, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.188
retrieve+0.125+0.250+0.188
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 250; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.875
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 61'
'synthetic question 61'
difficulty
0.199
0.199
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'hallucinated'
verify
'stale_fact'
'abstain'
q062 factual=0, v(∅)=0.50, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.094
retrieve+0.250+0.250+0.302
answer+0.000+0.000+0.052
verify+0.000+0.000+0.052

exact; 16 coalitions; cost 259; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}0.750
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.750
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.500
{rewrite, answer, verify}0.750
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 62'
'synthetic question 62'
difficulty
0.091
0.091
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q063 factual=0, v(∅)=0.12, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.292
retrieve+0.125+0.500+0.292
answer+0.125+0.375+0.250
verify+0.000+0.125+0.042
◆

exact; 16 coalitions; cost 301; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.625
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 63'
'synthetic question 63'
difficulty
0.58
0.58
rewrite
'wrong_entity'
'vague'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q064 factual=0, v(∅)=0.38, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.323
retrieve+0.125+0.250+0.198
answer+0.000+0.125+0.073
verify+0.000+0.000+0.031

exact; 16 coalitions; cost 271; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.625
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 64'
'synthetic question 64'
difficulty
0.299
0.299
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q066 factual=0, v(∅)=0.50, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.042
retrieve+0.375+0.250+0.292
answer+0.250+0.000+0.104
verify+0.125+0.000+0.062

exact; 16 coalitions; cost 231; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.875
{rewrite, retrieve}0.875
{answer}0.750
{rewrite, answer}0.750
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.750
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.750
{rewrite, answer, verify}0.750
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 66'
'synthetic question 66'
difficulty
0.2
0.2
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q067 factual=0, v(∅)=0.25, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.500+0.365
retrieve+0.125+0.250+0.177
answer+0.250+0.000+0.135
verify+0.125+0.000+0.073
◆

exact; 16 coalitions; cost 276; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}0.750
{retrieve, answer}0.500
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.500
{rewrite, retrieve, verify}1.000
{answer, verify}0.500
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 67'
'synthetic question 67'
difficulty
0.942
0.942
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q068 factual=0, v(∅)=0.25, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.156
retrieve+0.250+0.250+0.281
answer+0.250+0.000+0.156
verify+0.250+0.000+0.156
◆

exact; 16 coalitions; cost 242; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.500
{rewrite, answer}0.750
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.750
{retrieve, verify}0.875
{rewrite, retrieve, verify}1.000
{answer, verify}0.500
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 68'
'synthetic question 68'
difficulty
0.365
0.365
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q069 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.000+0.125
retrieve+0.375+0.250+0.312
answer+0.125+0.250+0.188
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 256; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 69'
'synthetic question 69'
difficulty
0.105
0.105
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q070 factual=0, v(∅)=0.50, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.135
retrieve+0.125+0.375+0.260
answer+0.000+0.125+0.094
verify+0.000+0.000+0.010

exact; 16 coalitions; cost 242; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 70'
'synthetic question 70'
difficulty
0.629
0.629
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q071 factual=0, v(∅)=0.25, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.188
retrieve+0.125+0.250+0.188
answer+0.125+0.250+0.188
verify+0.125+0.000+0.062
◆

exact; 16 coalitions; cost 257; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 71'
'synthetic question 71'
difficulty
0.927
0.927
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q072 factual=0, v(∅)=0.25, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.062
retrieve+0.000+0.250+0.125
answer+0.250+0.625+0.438
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 239; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.250
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 72'
'synthetic question 72'
difficulty
0.44
0.44
rewrite
'wrong_entity'
'vague'
retrieve
'near_miss'
'stale'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q073 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.292
retrieve+0.250+0.750+0.500
answer+0.000+0.125+0.062
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 293; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.750
{answer}0.125
{rewrite, answer}0.250
{retrieve, answer}0.500
{rewrite, retrieve, answer}1.000
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 73'
'synthetic question 73'
difficulty
0.955
0.955
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q074 factual=0, v(∅)=0.38, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.198
retrieve+0.125+0.250+0.198
answer+0.000+0.125+0.094
verify+0.000+0.000+0.010
◆

exact; 16 coalitions; cost 299; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 74'
'synthetic question 74'
difficulty
0.5
0.5
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q075 factual=0, v(∅)=0.12, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.375+0.417
retrieve+0.375+0.375+0.375
answer+0.125+0.000+0.062
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 307; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.625
{retrieve}0.500
{rewrite, retrieve}0.875
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.125
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}1.000
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 75'
'synthetic question 75'
difficulty
0.425
0.425
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q077 factual=0, v(∅)=0.12, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.271
retrieve+0.250+0.125+0.208
answer+0.250+0.250+0.271
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 280; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.500
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 77'
'synthetic question 77'
difficulty
0.995
0.995
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q078 factual=0, v(∅)=0.00, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.167
retrieve+0.125+0.375+0.229
answer+0.375+0.500+0.417
verify+0.125+0.000+0.062
◆

exact; 16 coalitions; cost 277; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.375
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 78'
'synthetic question 78'
difficulty
0.949
0.949
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q079 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.229
retrieve+0.375+0.375+0.354
answer+0.250+0.125+0.208
verify+0.125+0.000+0.083
◆

exact; 16 coalitions; cost 280; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 79'
'synthetic question 79'
difficulty
0.46
0.46
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q083 factual=0, v(∅)=0.25, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.500+0.271
retrieve+0.000+0.375+0.188
answer+0.125+0.375+0.271
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 310; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.500
{rewrite, retrieve, answer}1.000
{verify}0.250
{rewrite, verify}0.375
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 83'
'synthetic question 83'
difficulty
0.786
0.786
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q086 factual=0, v(∅)=0.12, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.188
retrieve+0.500+0.375+0.438
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 256; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 86'
'synthetic question 86'
difficulty
0.711
0.711
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q089 factual=0, v(∅)=0.12, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.500+0.490
retrieve+0.125+0.250+0.219
answer+0.000+0.125+0.115
verify+0.000+0.000+0.052
◆

exact; 16 coalitions; cost 305; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.250
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.750
{retrieve, answer}0.500
{rewrite, retrieve, answer}1.000
{verify}0.125
{rewrite, verify}0.750
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 89'
'synthetic question 89'
difficulty
0.729
0.729
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q090 factual=0, v(∅)=0.25, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.375+0.167
retrieve+0.000+0.500+0.250
answer+0.125+0.250+0.208
verify+0.125+0.000+0.125
◆

exact; 16 coalitions; cost 276; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 90'
'synthetic question 90'
difficulty
0.927
0.927
rewrite
'wrong_entity'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q091 factual=0, v(∅)=0.00, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.250
retrieve+0.125+0.250+0.208
answer+0.125+0.000+0.083
verify+0.250+0.125+0.208
◆

exact; 16 coalitions; cost 261; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.375
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.625
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 91'
'synthetic question 91'
difficulty
0.968
0.968
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q093 factual=0, v(∅)=0.00, v(all)=0.50, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.500+0.229
retrieve+0.000+0.500+0.229
answer+0.000+0.125+0.042
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 290; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.000
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.000
{retrieve, answer}0.000
{rewrite, retrieve, answer}0.500
{verify}0.000
{rewrite, verify}0.000
{retrieve, verify}0.000
{rewrite, retrieve, verify}0.375
{answer, verify}0.000
{rewrite, answer, verify}0.000
{retrieve, answer, verify}0.000
{rewrite, retrieve, answer, verify}0.500

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 93'
'synthetic question 93'
difficulty
0.864
0.864
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'stale'
answer
'hallucinated'
'stale_fact'
verify
'hallucinated'
'abstain'
q094 factual=0, v(∅)=0.38, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.177
retrieve+0.000+0.125+0.115
answer+0.000+0.125+0.094
verify+0.000+0.125+0.115

exact; 16 coalitions; cost 256; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 94'
'synthetic question 94'
difficulty
0.981
0.981
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q095 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.177
retrieve+0.125+0.375+0.260
answer+0.125+0.000+0.094
verify+0.250+0.125+0.219
◆

exact; 16 coalitions; cost 282; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.250
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 95'
'synthetic question 95'
difficulty
0.957
0.957
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q096 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.177
retrieve+0.250+0.250+0.302
answer+0.000+0.125+0.115
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 276; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 96'
'synthetic question 96'
difficulty
0.149
0.149
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q098 factual=0, v(∅)=0.25, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.125+0.000+0.062
answer+0.375+0.375+0.375
verify+0.125+0.000+0.062

exact; 16 coalitions; cost 223; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.375
{answer}0.625
{rewrite, answer}0.875
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.500
{answer, verify}0.625
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 98'
'synthetic question 98'
difficulty
0.89
0.89
rewrite
'precise'
'vague'
retrieve
'gold'
'near_miss'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q099 factual=0, v(∅)=0.38, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.177
retrieve+0.000+0.250+0.177
answer+0.000+0.000+0.073
verify+0.000+0.000+0.073
◆

exact; 16 coalitions; cost 273; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 99'
'synthetic question 99'
difficulty
0.822
0.822
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q100 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.146
retrieve+0.375+0.500+0.479
answer+0.000+0.125+0.104
verify+0.000+0.000+0.021

exact; 16 coalitions; cost 278; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 100'
'synthetic question 100'
difficulty
0.48
0.48
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q101 factual=0, v(∅)=0.50, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.146
retrieve+0.250+0.250+0.271
answer+0.000+0.000+0.042
verify+0.000+0.000+0.042

exact; 16 coalitions; cost 236; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}0.750
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.750
{retrieve, verify}0.875
{rewrite, retrieve, verify}1.000
{answer, verify}0.500
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 101'
'synthetic question 101'
difficulty
0.232
0.232
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q102 factual=0, v(∅)=0.38, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.146
◆
retrieve+0.000+0.000+0.021
answer+0.000+0.125+0.083
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 232; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.625
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.500
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 102'
'synthetic question 102'
difficulty
0.802
0.802
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q103 factual=0, v(∅)=0.12, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.219
retrieve+0.500+0.500+0.531
◆
answer+0.000+0.125+0.094
verify+0.000+0.000+0.031

exact; 16 coalitions; cost 309; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.125
{rewrite, answer}0.500
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 103'
'synthetic question 103'
difficulty
0.924
0.924
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q104 factual=0, v(∅)=0.25, v(all)=0.75, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.375+0.375+0.375
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 261; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.375
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.250
{rewrite, verify}0.375
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.250
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 104'
'synthetic question 104'
difficulty
0.266
0.266
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q105 factual=0, v(∅)=0.38, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.240
◆
retrieve+0.000+0.375+0.198
answer+0.125+0.000+0.094
verify+0.125+0.000+0.094

exact; 16 coalitions; cost 297; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}1.000
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 105'
'synthetic question 105'
difficulty
0.539
0.539
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q107 factual=0, v(∅)=0.12, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.208
retrieve+0.125+0.250+0.208
answer+0.250+0.375+0.333
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 294; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.500
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 107'
'synthetic question 107'
difficulty
0.931
0.931
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q108 factual=0, v(∅)=0.62, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.062
retrieve+0.000+0.125+0.062
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 191; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.625
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.625
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.625
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 108'
'synthetic question 108'
difficulty
0.041
0.041
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q109 factual=0, v(∅)=0.12, v(all)=0.50, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.125+0.250+0.188
◆
answer+0.125+0.125+0.125
verify+0.125+0.000+0.062

exact; 16 coalitions; cost 262; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.125
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.250
{rewrite, answer}0.250
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.500
{verify}0.250
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.375
{answer, verify}0.250
{rewrite, answer, verify}0.250
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.500

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 109'
'synthetic question 109'
difficulty
0.732
0.732
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q110 factual=0, v(∅)=0.12, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.312
retrieve+0.125+0.250+0.208
answer+0.000+0.000+0.021
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 287; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.625
{verify}0.125
{rewrite, verify}0.500
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 110'
'synthetic question 110'
difficulty
0.614
0.614
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q111 factual=0, v(∅)=0.50, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.042
◆
retrieve+0.000+0.125+0.125
answer+0.125+0.125+0.188
verify+0.000+0.000+0.021

exact; 16 coalitions; cost 240; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.500
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 111'
'synthetic question 111'
difficulty
0.028
0.028
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q113 factual=0, v(∅)=0.62, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.167
retrieve+0.375+0.250+0.292
answer-0.125+0.000-0.083
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 236; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.875
{retrieve}1.000
{rewrite, retrieve}1.000
{answer}0.500
{rewrite, answer}0.750
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.875
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.500
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 113'
'synthetic question 113'
difficulty
0.016
0.016
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q115 factual=0, v(∅)=0.50, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.125+0.375+0.271
answer+0.000+0.000+0.021
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 241; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.875
{rewrite, retrieve, verify}1.000
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 115'
'synthetic question 115'
difficulty
0.513
0.513
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q116 factual=0, v(∅)=0.12, v(all)=0.62, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.115
retrieve+0.125+0.125+0.198
answer+0.125+0.000+0.135
verify+0.000+0.000+0.052
◆

exact; 16 coalitions; cost 257; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.625
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 116'
'synthetic question 116'
difficulty
0.929
0.929
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q117 factual=0, v(∅)=0.62, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.042
retrieve+0.125+0.125+0.167
answer+0.125+0.125+0.167
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 261; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.875
{answer}0.750
{rewrite, answer}0.875
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.625
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.750
{rewrite, answer, verify}0.875
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 117'
'synthetic question 117'
difficulty
0.066
0.066
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q118 factual=0, v(∅)=0.25, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.260
retrieve+0.125+0.250+0.198
answer+0.000+0.125+0.073
verify+0.000+0.125+0.094
◆

exact; 16 coalitions; cost 268; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 118'
'synthetic question 118'
difficulty
0.841
0.841
rewrite
'vague'
'precise'
retrieve
'stale'
'stale'
answer
'stale_fact'
'abstain'
verify
'stale_fact'
'abstain'
q120 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.198
retrieve+0.375+0.125+0.260
answer+0.125+0.125+0.135
verify+0.000+0.000+0.031

exact; 16 coalitions; cost 273; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 120'
'synthetic question 120'
difficulty
0.344
0.344
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q121 factual=0, v(∅)=0.50, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.312
retrieve+0.250+0.125+0.188
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 233; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.875
{retrieve}0.750
{rewrite, retrieve}1.000
{answer}0.500
{rewrite, answer}0.875
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.500
{rewrite, verify}0.875
{retrieve, verify}0.750
{rewrite, retrieve, verify}1.000
{answer, verify}0.500
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 121'
'synthetic question 121'
difficulty
0.43
0.43
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q122 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.344
retrieve+0.250+0.500+0.406
answer+0.000+0.250+0.198
verify+0.000+0.000+0.052
◆

exact; 16 coalitions; cost 336; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.000
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.000
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 122'
'synthetic question 122'
difficulty
0.966
0.966
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q123 factual=0, v(∅)=0.38, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.281
retrieve+0.125+0.250+0.198
answer+0.000+0.125+0.115
verify+0.000+0.000+0.031

exact; 16 coalitions; cost 271; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 123'
'synthetic question 123'
difficulty
0.562
0.562
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q124 factual=0, v(∅)=0.25, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.188
retrieve+0.125+0.125+0.104
answer+0.375+0.125+0.250
verify+0.125+0.000+0.083
◆

exact; 16 coalitions; cost 246; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 124'
'synthetic question 124'
difficulty
0.259
0.259
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q126 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.302
retrieve+0.125+0.375+0.240
answer+0.250+0.375+0.302
verify+0.125+0.125+0.156
◆

exact; 16 coalitions; cost 325; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.500
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 126'
'synthetic question 126'
difficulty
0.888
0.888
rewrite
'precise'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q127 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.021
retrieve+0.250+0.375+0.354
answer+0.375+0.000+0.229
verify+0.250+0.000+0.146
◆

exact; 16 coalitions; cost 245; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.125
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.500
{rewrite, answer}0.500
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.375
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 127'
'synthetic question 127'
difficulty
0.226
0.226
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q128 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.312
retrieve+0.250+0.625+0.438
answer+0.125+0.375+0.250
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 284; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.625
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 128'
'synthetic question 128'
difficulty
0.125
0.125
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q129 factual=0, v(∅)=0.50, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.062
retrieve+0.250+0.125+0.188
answer+0.000+0.000+0.000
verify+0.125+0.125+0.125
◆

exact; 16 coalitions; cost 196; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.625
{rewrite, verify}0.750
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 129'
'synthetic question 129'
difficulty
0.288
0.288
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'hallucinated'
verify
'stale_fact'
'correct'
q130 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.125+0.094
retrieve+0.125+0.500+0.365
answer+0.375+0.250+0.365
verify+0.250+0.000+0.177
◆

exact; 16 coalitions; cost 270; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.000
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.250
{rewrite, verify}0.375
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 130'
'synthetic question 130'
difficulty
0.586
0.586
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'near_miss'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q131 factual=0, v(∅)=0.38, v(all)=0.62, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.083
◆
retrieve+0.000+0.000+0.021
answer+0.250+0.000+0.146
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 242; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.625
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.625
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 131'
'synthetic question 131'
difficulty
0.554
0.554
rewrite
'vague'
'precise'
retrieve
'near_miss'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q132 factual=0, v(∅)=0.25, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.500+0.271
retrieve+0.000+0.500+0.208
answer+0.000+0.125+0.062
verify+0.000+0.125+0.083
◆

exact; 16 coalitions; cost 274; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.250
{rewrite, retrieve}0.375
{answer}0.250
{rewrite, answer}0.375
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.750
{verify}0.250
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.250
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 132'
'synthetic question 132'
difficulty
0.81
0.81
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q133 factual=0, v(∅)=0.25, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.375+0.396
retrieve+0.250+0.125+0.188
answer+0.000+0.000+0.021
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 299; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.625
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.750
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.750
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 133'
'synthetic question 133'
difficulty
0.56
0.56
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q135 factual=0, v(∅)=0.38, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.156
◆
retrieve+0.000+0.375+0.240
answer+0.000+0.000+0.052
verify+0.000+0.000+0.052

exact; 16 coalitions; cost 271; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 135'
'synthetic question 135'
difficulty
0.413
0.413
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q136 factual=0, v(∅)=0.12, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.135
retrieve+0.125+0.250+0.219
answer+0.125+0.250+0.240
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 268; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.250
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.500
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 136'
'synthetic question 136'
difficulty
0.818
0.818
rewrite
'wrong_entity'
'vague'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q137 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.219
retrieve+0.250+0.375+0.344
answer+0.000+0.000+0.031
verify+0.000+0.000+0.031

exact; 16 coalitions; cost 298; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 137'
'synthetic question 137'
difficulty
0.627
0.627
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q140 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.240
retrieve+0.125+0.500+0.302
answer+0.125+0.250+0.198
verify+0.000+0.000+0.010

exact; 16 coalitions; cost 271; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.375
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.625
{answer, verify}0.250
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 140'
'synthetic question 140'
difficulty
0.553
0.553
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q142 factual=0, v(∅)=0.00, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.250
retrieve+0.250+0.250+0.250
answer+0.125+0.000+0.062
verify+0.125+0.000+0.062

exact; 16 coalitions; cost 251; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.625
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 142'
'synthetic question 142'
difficulty
0.848
0.848
rewrite
'precise'
'wrong_entity'
retrieve
'near_miss'
'irrelevant'
answer
'abstain'
'abstain'
verify
'abstain'
'abstain'
q143 factual=0, v(∅)=0.62, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.083
retrieve+0.125+0.125+0.083
answer+0.250+0.125+0.146
verify+0.125+0.000+0.062

exact; 16 coalitions; cost 247; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.750
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.875
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.750
{rewrite, verify}0.875
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.875
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 143'
'synthetic question 143'
difficulty
0.145
0.145
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q145 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.188
retrieve+0.250+0.375+0.333
◆
answer+0.000+0.125+0.083
verify+0.000+0.000+0.021

exact; 16 coalitions; cost 309; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.250
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 145'
'synthetic question 145'
difficulty
0.91
0.91
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q146 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.250
retrieve+0.500+0.250+0.375
answer+0.125+0.000+0.062
verify+0.125+0.000+0.062
◆

exact; 16 coalitions; cost 268; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.250
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 146'
'synthetic question 146'
difficulty
0.043
0.043
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'near_miss'
answer
'hallucinated'
'stale_fact'
verify
'hallucinated'
'abstain'
q148 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.000+0.125
retrieve+0.500+0.375+0.458
answer+0.000+0.000+0.021
verify+0.000+0.000+0.021

exact; 16 coalitions; cost 262; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.625
{retrieve}0.875
{rewrite, retrieve}0.875
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}1.000
{rewrite, retrieve, verify}1.000
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 148'
'synthetic question 148'
difficulty
0.415
0.415
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q150 factual=0, v(∅)=0.62, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.104
retrieve+0.125+0.125+0.104
◆
answer+0.250+0.000+0.104
verify+0.125+0.000+0.062

exact; 16 coalitions; cost 273; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.750
{retrieve}0.750
{rewrite, retrieve}0.875
{answer}0.875
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.750
{rewrite, verify}0.875
{retrieve, verify}0.875
{rewrite, retrieve, verify}1.000
{answer, verify}0.875
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 150'
'synthetic question 150'
difficulty
0.01
0.01
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q151 factual=0, v(∅)=0.25, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.167
retrieve+0.000+0.250+0.146
answer+0.250+0.125+0.229
verify+0.125+0.000+0.083
◆

exact; 16 coalitions; cost 254; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.500
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 151'
'synthetic question 151'
difficulty
0.365
0.365
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q153 factual=0, v(∅)=0.50, v(all)=0.62, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.062
retrieve+0.125+0.000+0.062
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 217; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.625
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.625

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 153'
'synthetic question 153'
difficulty
0.653
0.653
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q155 factual=0, v(∅)=0.50, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.000
retrieve+0.000+0.000+0.000
answer+0.250+0.000+0.125
verify+0.250+0.000+0.125
◆

exact; 16 coalitions; cost 203; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.750
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.750
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.750
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 155'
'synthetic question 155'
difficulty
0.703
0.703
rewrite
'wrong_entity'
'vague'
retrieve
'irrelevant'
'near_miss'
answer
'hallucinated'
'abstain'
verify
'hallucinated'
'abstain'
q156 factual=0, v(∅)=0.25, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.250+0.375
retrieve+0.250+0.000+0.125
answer+0.250+0.125+0.187
verify+0.125+0.000+0.062
◆

exact; 16 coalitions; cost 302; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.750
{retrieve}0.500
{rewrite, retrieve}0.750
{answer}0.500
{rewrite, answer}1.000
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.875
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 156'
'synthetic question 156'
difficulty
0.944
0.944
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q158 factual=0, v(∅)=0.12, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.271
retrieve+0.000+0.250+0.146
answer+0.250+0.125+0.208
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 259; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.125
{rewrite, retrieve}0.625
{answer}0.375
{rewrite, answer}0.500
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.250
{retrieve, verify}0.125
{rewrite, retrieve, verify}0.625
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 158'
'synthetic question 158'
difficulty
0.865
0.865
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q159 factual=0, v(∅)=0.62, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.000+0.021
retrieve+0.000+0.250+0.167
answer+0.000+0.125+0.104
verify+0.125+0.000+0.083
◆

exact; 16 coalitions; cost 251; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.625
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}1.000
{rewrite, retrieve, answer}1.000
{verify}0.750
{rewrite, verify}0.750
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}1.000
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 159'
'synthetic question 159'
difficulty
0.059
0.059
rewrite
'vague'
'precise'
retrieve
'near_miss'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q162 factual=0, v(∅)=0.25, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.500+0.521
retrieve+0.125+0.000+0.104
answer+0.000+0.000+0.083
verify+0.000+0.000+0.042
◆

exact; 16 coalitions; cost 302; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.625
{retrieve}0.375
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}1.000
{retrieve, answer}0.500
{rewrite, retrieve, answer}1.000
{verify}0.250
{rewrite, verify}0.875
{retrieve, verify}0.375
{rewrite, retrieve, verify}1.000
{answer, verify}0.250
{rewrite, answer, verify}1.000
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 162'
'synthetic question 162'
difficulty
0.489
0.489
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q163 factual=0, v(∅)=0.12, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.302
retrieve+0.125+0.375+0.260
answer+0.000+0.000+0.031
verify+0.000+0.000+0.031

exact; 16 coalitions; cost 284; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.125
{rewrite, answer}0.375
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.375
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.375
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 163'
'synthetic question 163'
difficulty
0.976
0.976
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q165 factual=0, v(∅)=0.12, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.500+0.250+0.375
retrieve+0.250+0.125+0.188
answer+0.000+0.125+0.062
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 267; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.625
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.625
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.625
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 165'
'synthetic question 165'
difficulty
0.309
0.309
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q166 factual=0, v(∅)=0.50, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.125
retrieve+0.250+0.250+0.250
answer+0.000+0.000+0.000
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 245; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.750
{rewrite, retrieve}0.875
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 166'
'synthetic question 166'
difficulty
0.27
0.27
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q167 factual=0, v(∅)=0.50, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.062
◆
retrieve+0.125+0.125+0.125
answer+0.125+0.000+0.062
verify+0.125+0.125+0.125

exact; 16 coalitions; cost 228; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.500
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.750
{verify}0.625
{rewrite, verify}0.750
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 167'
'synthetic question 167'
difficulty
0.863
0.863
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q169 factual=0, v(∅)=0.12, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.229
retrieve+0.500+0.250+0.354
answer+0.125+0.250+0.167
verify+0.000+0.000+0.000

exact; 16 coalitions; cost 273; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.500
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 169'
'synthetic question 169'
difficulty
0.511
0.511
rewrite
'precise'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q170 factual=0, v(∅)=0.25, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.000+0.125
retrieve+0.250+0.000+0.125
answer+0.375+0.250+0.312
verify+0.125+0.000+0.062
◆

exact; 16 coalitions; cost 260; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.625
{rewrite, answer}0.875
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.625
{answer, verify}0.625
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 170'
'synthetic question 170'
difficulty
0.344
0.344
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q171 factual=0, v(∅)=0.38, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.292
retrieve+0.250+0.125+0.167
answer+0.000+0.125+0.042
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 254; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.750
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 171'
'synthetic question 171'
difficulty
0.995
0.995
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q172 factual=0, v(∅)=0.25, v(all)=0.88, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.000+0.062
retrieve+0.250+0.125+0.188
answer+0.375+0.125+0.250
verify+0.250+0.000+0.125

exact; 16 coalitions; cost 214; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.375
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.625
{rewrite, answer}0.750
{retrieve, answer}0.875
{rewrite, retrieve, answer}0.875
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.750
{answer, verify}0.625
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 172'
'synthetic question 172'
difficulty
0.316
0.316
rewrite
'wrong_entity'
'precise'
retrieve
'near_miss'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q173 factual=0, v(∅)=0.00, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.229
retrieve+0.750+0.250+0.500
answer+0.375+0.125+0.250
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 318; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.750
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.875
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.875
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 173'
'synthetic question 173'
difficulty
0.183
0.183
rewrite
'vague'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q174 factual=0, v(∅)=0.25, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.281
retrieve+0.000+0.125+0.094
answer+0.000+0.125+0.094
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 285; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.750
{verify}0.250
{rewrite, verify}0.625
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.625
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 174'
'synthetic question 174'
difficulty
0.88
0.88
rewrite
'precise'
'vague'
retrieve
'irrelevant'
'near_miss'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'abstain'
q175 factual=0, v(∅)=0.00, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.625+0.490
retrieve+0.125+0.250+0.198
answer+0.125+0.375+0.281
verify+0.000+0.000+0.031
◆

exact; 16 coalitions; cost 322; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.000
{rewrite}0.375
{retrieve}0.125
{rewrite, retrieve}0.375
{answer}0.125
{rewrite, answer}0.750
{retrieve, answer}0.375
{rewrite, retrieve, answer}1.000
{verify}0.000
{rewrite, verify}0.375
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.625
{answer, verify}0.125
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 175'
'synthetic question 175'
difficulty
0.812
0.812
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q176 factual=0, v(∅)=0.25, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.219
retrieve+0.250+0.375+0.302
answer+0.000+0.125+0.073
verify+0.125+0.125+0.156
◆

exact; 16 coalitions; cost 259; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.500
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 176'
'synthetic question 176'
difficulty
0.668
0.668
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q177 factual=0, v(∅)=0.38, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.250+0.292
retrieve+0.250+0.125+0.208
answer+0.000+0.125+0.104
verify+0.000+0.000+0.021
◆

exact; 16 coalitions; cost 301; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.875
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 177'
'synthetic question 177'
difficulty
0.958
0.958
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q178 factual=0, v(∅)=0.12, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.365
retrieve+0.375+0.125+0.281
answer+0.000+0.000+0.052
verify+0.000+0.000+0.052
◆

exact; 16 coalitions; cost 307; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.500
{retrieve}0.500
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.750
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.875
{verify}0.125
{rewrite, verify}0.750
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.125
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 178'
'synthetic question 178'
difficulty
0.926
0.926
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q179 factual=0, v(∅)=0.12, v(all)=0.75, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.000+0.250+0.125
retrieve+0.000+0.250+0.125
answer+0.125+0.250+0.188
verify+0.125+0.250+0.188
◆

exact; 16 coalitions; cost 254; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.125
{retrieve}0.125
{rewrite, retrieve}0.250
{answer}0.250
{rewrite, answer}0.250
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.500
{verify}0.250
{rewrite, verify}0.375
{retrieve, verify}0.250
{rewrite, retrieve, verify}0.500
{answer, verify}0.375
{rewrite, answer, verify}0.500
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 179'
'synthetic question 179'
difficulty
0.748
0.748
rewrite
'vague'
'precise'
retrieve
'stale'
'near_miss'
answer
'stale_fact'
'abstain'
verify
'stale_fact'
'abstain'
q181 factual=0, v(∅)=0.12, v(all)=1.00, top: answer
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.177
retrieve+0.250+0.125+0.219
answer+0.250+0.125+0.240
verify+0.250+0.125+0.240
◆

exact; 16 coalitions; cost 257; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.375
{rewrite, retrieve}0.375
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.875
{retrieve, answer, verify}0.875
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 181'
'synthetic question 181'
difficulty
0.247
0.247
rewrite
'precise'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q182 factual=0, v(∅)=0.25, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.125+0.167
retrieve+0.125+0.250+0.188
answer+0.250+0.125+0.188
verify+0.125+0.000+0.083
◆

exact; 16 coalitions; cost 271; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.500
{retrieve}0.375
{rewrite, retrieve}0.500
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.750
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 182'
'synthetic question 182'
difficulty
0.141
0.141
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q183 factual=0, v(∅)=0.12, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.500+0.396
retrieve+0.250+0.125+0.208
answer+0.000+0.125+0.083
verify+0.000+0.125+0.062
◆

exact; 16 coalitions; cost 307; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.375
{rewrite, retrieve}0.625
{answer}0.125
{rewrite, answer}0.625
{retrieve, answer}0.375
{rewrite, retrieve, answer}0.750
{verify}0.125
{rewrite, verify}0.500
{retrieve, verify}0.375
{rewrite, retrieve, verify}0.750
{answer, verify}0.125
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.375
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 183'
'synthetic question 183'
difficulty
0.67
0.67
rewrite
'wrong_entity'
'precise'
retrieve
'stale'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q184 factual=0, v(∅)=0.38, v(all)=0.88, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.125+0.115
retrieve+0.250+0.250+0.240
answer+0.125+0.000+0.073
verify+0.125+0.000+0.073

exact; 16 coalitions; cost 225; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.625
{answer}0.500
{rewrite, answer}0.625
{retrieve, answer}0.750
{rewrite, retrieve, answer}0.875
{verify}0.500
{rewrite, verify}0.625
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.500
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 184'
'synthetic question 184'
difficulty
0.715
0.715
rewrite
'vague'
'precise'
retrieve
'irrelevant'
'gold'
answer
'stale_fact'
'correct'
verify
'stale_fact'
'correct'
q185 factual=0, v(∅)=0.25, v(all)=0.75, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.125+0.250
retrieve+0.375+0.125+0.250
answer+0.000-0.125-0.062
verify+0.125+0.000+0.062
◆

exact; 16 coalitions; cost 259; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.250
{rewrite, answer}0.625
{retrieve, answer}0.625
{rewrite, retrieve, answer}0.750
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}0.875
{answer, verify}0.250
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.625
{rewrite, retrieve, answer, verify}0.750

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 185'
'synthetic question 185'
difficulty
0.167
0.167
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q187 factual=0, v(∅)=0.12, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.375+0.260
retrieve+0.125+0.250+0.198
answer+0.125+0.000+0.073
verify+0.125+0.250+0.219
◆

exact; 16 coalitions; cost 256; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.250
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.250
{rewrite, answer}0.375
{retrieve, answer}0.250
{rewrite, retrieve, answer}0.625
{verify}0.250
{rewrite, verify}0.500
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 187'
'synthetic question 187'
difficulty
0.91
0.91
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'hallucinated'
verify
'hallucinated'
'correct'
q188 factual=0, v(∅)=0.38, v(all)=1.00, top: retrieve
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.125+0.250+0.240
retrieve+0.250+0.250+0.281
answer+0.000+0.000+0.052
verify+0.000+0.000+0.052

exact; 16 coalitions; cost 256; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.375
{rewrite}0.500
{retrieve}0.625
{rewrite, retrieve}0.750
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.375
{rewrite, verify}0.750
{retrieve, verify}0.750
{rewrite, retrieve, verify}1.000
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 188'
'synthetic question 188'
difficulty
0.561
0.561
rewrite
'wrong_entity'
'precise'
retrieve
'irrelevant'
'gold'
answer
'hallucinated'
'correct'
verify
'hallucinated'
'correct'
q191 factual=0, v(∅)=0.25, v(all)=1.00, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.375+0.250+0.312
retrieve+0.375+0.250+0.312
answer+0.125+0.125+0.125
verify+0.000+0.000+0.000
◆

exact; 16 coalitions; cost 262; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.250
{rewrite}0.625
{retrieve}0.625
{rewrite, retrieve}0.875
{answer}0.375
{rewrite, answer}0.750
{retrieve, answer}0.750
{rewrite, retrieve, answer}1.000
{verify}0.250
{rewrite, verify}0.625
{retrieve, verify}0.625
{rewrite, retrieve, verify}0.875
{answer, verify}0.375
{rewrite, answer, verify}0.750
{retrieve, answer, verify}0.750
{rewrite, retrieve, answer, verify}1.000

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 191'
'synthetic question 191'
difficulty
0.526
0.526
rewrite
'precise'
'precise'
retrieve
'gold'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'
q192 factual=0, v(∅)=0.12, v(all)=0.88, top: rewrite
stepfix aloneleave-one-outShapleyShapley bar (±CI)last touch
rewrite+0.250+0.375+0.292
retrieve+0.125+0.250+0.167
answer+0.250+0.125+0.167
verify+0.250+0.000+0.125
◆

exact; 16 coalitions; cost 270; exhaustive

Coalition values v(S) (S = set of fixed steps):

{}0.125
{rewrite}0.375
{retrieve}0.250
{rewrite, retrieve}0.500
{answer}0.375
{rewrite, answer}0.625
{retrieve, answer}0.500
{rewrite, retrieve, answer}0.875
{verify}0.375
{rewrite, verify}0.625
{retrieve, verify}0.500
{rewrite, retrieve, verify}0.750
{answer, verify}0.375
{rewrite, answer, verify}0.625
{retrieve, answer, verify}0.500
{rewrite, retrieve, answer, verify}0.875

Outputs: factual vs. all-fixed

valuefactualall fixes
question
'synthetic question 192'
'synthetic question 192'
difficulty
0.523
0.523
rewrite
'vague'
'precise'
retrieve
'stale'
'gold'
answer
'abstain'
'correct'
verify
'abstain'
'correct'

… 4 more cases omitted.

Variance: common random numbers vs independent re-sampling

3) Variance of per-case blame estimates: 100 failing cases, 4 worlds per coalition, 8 replicates
mode      estimator     Var CRN  Var indep  indep/CRN  cost CRN  cost indep  Var*cost   mean estimate, CRN (rewrite, retrieve, answer, verify)
posterior fix-alone     0.02567    0.02134      0.83x      (by-product of exact-avg)   [0.214, 0.235, 0.149, 0.068]
posterior exact-avg     0.01303    0.00920      0.71x     15314       67800     3.13x   [0.285, 0.304, 0.176, 0.074]
posterior mc-perm       0.00947    0.01903      2.01x     36720       67962     3.72x   [0.294, 0.314, 0.169, 0.067]
prior     fix-alone     0.02905    0.10150      3.49x      (by-product of exact-avg)   [0.158, 0.191, 0.106, 0.058]
prior     exact-avg     0.01797    0.01555      0.87x     13422       67200     4.33x   [0.206, 0.248, 0.131, 0.061]
prior     mc-perm       0.01021    0.02858      2.80x     34872       67962     5.46x   [0.202, 0.262, 0.133, 0.053]
Var = variance across replicates, averaged over cases and steps; cost = step cost units charged per replicate (cache hits are free); Var*cost = (Var*cost)_indep / (Var*cost)_CRN, i.e. efficiency gain of CRN at equal budget. Recorded-noise replay has zero estimator variance (it is deterministic).

Legend: fix alone = v({i}) − v(∅); leave-one-out = v(all) − v(all∖{i}); Shapley splits v(all) − v(∅) fairly over all orders of applying fixes; ◆ = naive last-step-to-touch blame. Generated by agentblame.