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Why the fun9 well is closed only partly (diagnostics only, method unchanged). The well itself IS closed: reaching the root's side takes 4 evaluations with contra/defect against Chandrupatla's 3 (13 and 33 before). The remaining +20 (75 vs 55) is after it: (1) the exponential flank on the widest brackets - our step moves ~1 per evaluation down exp(x) (f/f' = 1), 10 evaluations where Chandrupatla halves 3 times; the analogy entry comes late because exp is self-similar by TRANSLATION, not scaling - the pair's x-scale does not shrink, so m = ln(f ratio)/ln(x ratio) is undefined or negative; (2) overconfident near-zero steps - on a steep flank the three-point slope is huge, z ~ 0, S ~ 1, the model promises the root at a point that is not it: 8 wasted evaluations on fun9 (27 without the decisions).

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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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vvs
2026-09-21 18:35:07 +01:00
co-authored by Claude Opus 5
parent 08863c170c
commit 485f25f165
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results_diag_fun9_well.txt
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problem method n to first f>0 after refused forced
fun9.1 Chandrupatla 8 4 4
none 8 4 4 0 0
contra 8 4 4 0 0
defect 8 4 4 0 0
contra+flatanalogmempt 8 4 4 0 0
defect+flatanalogmempt 8 4 4 0 0
fun9.2 Chandrupatla 9 3 6
none 11 4 7 0 0
contra 11 4 7 1 0
defect 11 4 7 2 0
contra+flatanalogmempt 11 4 7 1 0
defect+flatanalogmempt 11 4 7 2 0
fun9.3 Chandrupatla 11 3 8
none 21 13 8 0 0
contra 15 4 11 1 0
defect 14 4 10 2 0
contra+flatanalogmempt 15 4 11 1 0
defect+flatanalogmempt 14 4 10 2 0
fun9.4 Chandrupatla 13 3 10
none 39 33 6 0 0
contra 21 4 17 1 0
defect 17 4 13 2 0
contra+flatanalogmempt 21 4 17 1 0
defect+flatanalogmempt 17 4 13 2 0
fun9.5 Chandrupatla 14 3 11
none 26 3 23 0 0
contra 26 3 23 0 0
defect 26 3 23 1 0
contra+flatanalogmempt 25 3 22 4 0
defect+flatanalogmempt 25 3 22 5 0
diag done
== none
group problems evals near-zero wasted
APS 154 2634 425 30
CHA-flat 20 1823 695 188
CHA-fun1 5 99 44 3
CHA-fun2 5 141 18 3
CHA-fun7 5 137 99 12
CHA-fun8 5 52 15 0
CHA-fun9 5 105 56 27
== defect+flatanalogmempt
group problems evals near-zero wasted
APS 154 2384 438 52
CHA-flat 20 789 447 147
CHA-fun1 5 99 19 4
CHA-fun2 5 144 13 2
CHA-fun7 5 134 91 41
CHA-fun8 5 57 16 0
CHA-fun9 5 75 22 8
diag done