the wide-bracket gap is NOT closed, and now it has an address: the STEP RULE, not the guarantee and not the reading places. fun1 is one function at growing widths — 7/8, 12/12, 19/15, 59/24, 63/44 — so we tie when narrow and lose as it widens, while our observed order is the HIGHER one (3.63 vs 2.02); 59 on a 2e4 bracket is what bisection needs, i.e. one halving per evaluation against their 2.3. With the safeguard removed entirely we still spend 46/57/61/68 against bisection 57/77/45/45 and Chandrupatla 24/44 — worse than bisection on two of them. |f|/|f'| is an absolute length and cannot march across decades; written into the paper as the stated limit. Also fixed a tracer bug that had best_of double-counting evaluations (2993 vs 1487)

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-09-21 00:09:18 +01:00
parent 8d20816163
commit 0fb75be3cf
8 changed files with 372 additions and 6 deletions
@@ -0,0 +1,11 @@
+problem                      bracket       root      m  ours n    ord   CH n    ord
+fun1.1    [         2,          3]     2.0946   1.00       7   4.28      8   1.80
+          |f| at root+1e-5 = 1.116e-04, root+1e-2 = 1.122e-01, ours x=+2.094551482 ok=True
+fun1.2    [         1,         10]     2.0946   1.00      12   1.87     12   1.81
+          |f| at root+1e-5 = 1.116e-04, root+1e-2 = 1.122e-01, ours x=+2.094551482 ok=True
+fun1.3    [         1,        100]     2.0946   1.00      19   2.46     15   1.67
+          |f| at root+1e-5 = 1.116e-04, root+1e-2 = 1.122e-01, ours x=+2.094551482 ok=True
+fun1.4    [    -1e+04,      1e+04]     2.0946   1.00      59   3.63     24   2.02
+          |f| at root+1e-5 = 1.116e-04, root+1e-2 = 1.122e-01, ours x=+2.094551482 ok=True
+fun1.5    [    -1e+10,      1e+10]     2.0946   1.00      63   1.85     44   2.20
+          |f| at root+1e-5 = 1.116e-04, root+1e-2 = 1.122e-01, ours x=+2.094551482 ok=True