Audit on Valeri's challenge: our Chandrupatla implementation stops below 2*xtol (tl = tol/span > 1/2) while every other method, SciPy's included, stops at xtol; the protocol corrected that factor for ITP and not here, and best_of let the looser run win. Corrected it costs Chandrupatla 2 evaluations on APS (2785 -> 2787) and 18 on CHA (2423 -> 2441): real, in the competitor's favour, and not what changes the picture. The public scipy.optimize.elementwise.find_root, the private _chandrupatla and ours corrected agree on all 199 problems exactly.

What the tables' totals hid: problem by problem the scheduled projection beats Chandrupatla on APS 87/24/42, exact sign test p = 9e-5, while trailing by 0.7% in total; on CHA Chandrupatla is genuinely better (26 to 9, p = 0.006). The earned projection ties him on APS problems (79/3/71, p = 0.57). Benchmark not yet switched to the library baseline - awaiting Valeri's decision together with the framing of the proposed method. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-09-21 10:14:42 +01:00
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+Chandrupatla                          APS  solved    CHA  solved   both
+ours @ xtol (as benchmarked)         2785  153/154   2424   40/45   5209
+ours @ xtol/2 (ITP's correction)     2787  153/154   2441   40/45   5228
+scipy @ xtol                         2787  153/154   2441   40/45   5228
+best_of, as benchmarked              2785  153/154   2423   40/45   5208
+best_of, corrected                   2787  153/154   2441   40/45   5228
+
+our implementation, largest final bracket width / xtol over all problems: 1000000000000.000
+(everyone else stops at <= 1; a value up to 2 confirms the looser rule)