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>
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@@ -0,0 +1,63 @@
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problem ours app/end CH app/end gap app gap end
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fun1.1 5/2 6/2 -1 +0
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fun1.2 10/2 10/2 +0 +0
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fun1.3 11/8 13/2 -2 +6
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fun1.4 20/39 21/3 -1 +36
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fun1.5 3/60 3/41 +0 +19
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fun2.1 7/2 7/2 +0 +0
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fun2.2 23/3 20/3 +3 +0
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fun2.3 27/3 25/4 +2 -1
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fun2.4 1/42 2/40 -1 +2
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fun2.5 1/48 2/47 -1 +1
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fun3.1 32/32 21/23 +11 +9
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fun3.2 28/28 23/23 +5 +5
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fun3.3 31/35 28/32 +3 +3
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fun3.4 31/42 28/41 +3 +1
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fun3.5 3/82 3/79 +0 +3
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fun4.1 30/24 21/23 +9 +1
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fun4.2 30/26 23/23 +7 +3
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fun4.3 32/38 29/27 +3 +11
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fun4.4 28/45 30/37 -2 +8
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fun4.5 3/83 3/77 +0 +6
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fun5.1 30/27 22/22 +8 +5
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fun5.2 28/26 22/22 +6 +4
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fun5.3 27/28 22/23 +5 +5
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fun5.4 31/26 22/25 +9 +1
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fun5.5 31/28 22/26 +9 +2
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fun6.1 29/23 22/22 +7 +1
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fun6.2 29/25 22/22 +7 +3
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fun6.3 25/25 22/23 +3 +2
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fun6.4 25/27 22/25 +3 +2
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fun6.5 25/30 22/26 +3 +4
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fun7.1 11/0 8/0 +3 +0
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fun7.2 11/0 8/0 +3 +0
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fun7.3 11/0 11/0 +0 +0
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fun7.4 11/0 18/0 -7 +0
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fun7.5 13/0 19/0 -6 +0
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fun8.1 11/2 8/2 +3 +0
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fun8.2 9/2 9/2 +0 +0
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fun8.3 10/2 10/3 +0 -1
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fun8.4 13/3 12/2 +1 +1
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fun8.5 16/2 13/2 +3 +0
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fun9.1 6/2 6/2 +0 +0
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fun9.2 10/2 7/2 +3 +0
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fun9.3 11/3 9/2 +2 +1
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fun9.4 13/2 10/3 +3 -1
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fun9.5 16/3 12/2 +4 +1
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skipped (not scorable under either criterion): []
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ours approach 808 endgame 932 total 1740 (46% of the cost is approach)
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chandrupatla approach 698 endgame 789 total 1487 (47% of the cost is approach)
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GAP: approach +110, endgame +143 (total +253)
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per family (approach gap / endgame gap):
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fun1 approach -4 endgame +61
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fun5 approach +37 endgame +17
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fun4 approach +17 endgame +29
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fun3 approach +22 endgame +21
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fun6 approach +23 endgame +12
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fun9 approach +12 endgame +1
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fun8 approach +7 endgame +0
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fun2 approach +3 endgame +2
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fun7 approach -7 endgame +0
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