CORRECTION, prompted by Valeri: the step IS a fraction of the bracket — with the ratio similarity 1-S = min(1,|f|/(|f'|D)) so step = min(D,|f|/|f'|) — and my 'absolute length cannot march' was wrong, as was the follow-up guess that we creep along one side: measured, 91.5% of our probes DO shrink the bracket, more often than Chandrupatla's 87.5%. What differs is how much each probe removes: 0.93 halvings per evaluation against 2.26. A linear model of the value axis undershoots on a wide bracket of a convex function, so the new bracket is about half; inverse quadratic interpolation lands near the root and removes four fifths. The limit is the ORDER OF THE MODEL the similarity is read against, and all three parameter-free ways round it are now measured failures (cbrt, log change of variable, derived3_m). Paper corrected

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-09-21 00:12:58 +01:00
parent 0fb75be3cf
commit 08ffa42e98
4 changed files with 143 additions and 9 deletions
@@ -0,0 +1,11 @@
+problem   method          evals  probes that shrank   share  halvings/eval
+fun1.3    ours               19                  15   78.9%          2.498
+fun1.3    chandrupatla       15                  13   86.7%          3.099
+fun1.4    ours               59                  54   91.5%          0.930
+fun1.4    chandrupatla       24                  21   87.5%          2.256
+fun1.5    ours               63                  60   95.2%          1.179
+fun1.5    chandrupatla       44                  41   93.2%          1.684
+fun3.1    ours               64                  61   95.3%          0.672
+fun3.1    chandrupatla       44                  42   95.5%          0.955
+fun5.1    ours               57                  47   82.5%          0.741
+fun5.1    chandrupatla       44                  42   95.5%          0.955