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PREREG_roots_jl outcome (server): variant A does NOT transfer by the stop rule on the Roots.jl / ModAB benchmark. 78 out-of-sample problems: total 1464 vs Chandrupatla 1566 (-6.5%, R1 holds), per problem 38/10/30 p=0.4 (R2 fails), guarantee held and all solved (R3); strict f24-f91 the same picture (1340 vs 1454, 35/6/25 p=0.25). B does not transfer either (32/11/35). Same structure as the first new corpus: multiple/flat roots 331 vs 481 (10:3); the rest 1133 vs 1085, per problem 28/10/27 - parity. Largest loss f32 (4 - tan x near the pole, 41 vs 12). Against Brent and TOMS748 A wins (47/25 p=0.013, 55/20 p=6e-5); they break the 2x-bisection bound on 11 and 9 problems, A on none.

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Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
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2026-09-21 19:40:05 +01:00
co-authored by Claude Opus 5
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== MAIN (78 out-of-sample)
base total 1884 solved 78/78 violations 0
A total 1464 solved 78/78 violations 0
B total 1537 solved 78/78 violations 0
chandrupatla total 1566 solved 78/78 violations 0
brent total 2455 solved 78/78 violations 11
toms748 total 2339 solved 78/78 violations 9
A: R1 ✓ (1464 vs 1566) R2 ✗ (38/10/30 p=0.4) R3 ✓ (viol 0, solved 78 vs 78) -> does NOT transfer
vs brent total 1464 vs 2455 per problem 47/6/25 p=0.013
vs toms748 total 1464 vs 2339 per problem 55/3/20 p=6.5e-05
B: R1 ✓ (1537 vs 1566) R2 ✗ (32/11/35 p=0.81) R3 ✓ (viol 0, solved 78 vs 78) -> does NOT transfer
vs brent total 1537 vs 2455 per problem 43/9/26 p=0.053
vs toms748 total 1537 vs 2339 per problem 46/6/26 p=0.024
== STRICT (f24-f91, out-of-sample)
base total 1734 solved 66/66 violations 0
A total 1340 solved 66/66 violations 0
B total 1385 solved 66/66 violations 0
chandrupatla total 1454 solved 66/66 violations 0
brent total 2333 solved 66/66 violations 11
toms748 total 2216 solved 66/66 violations 9
A: R1 ✓ (1340 vs 1454) R2 ✗ (35/6/25 p=0.25) R3 ✓ (viol 0, solved 66 vs 66)
vs brent total 1340 vs 2333 per problem 41/3/22 p=0.023
vs toms748 total 1340 vs 2216 per problem 48/2/16 p=7.7e-05
B: R1 ✓ (1385 vs 1454) R2 ✗ (29/7/30 p=1) R3 ✓ (viol 0, solved 66 vs 66)
vs brent total 1385 vs 2333 per problem 37/8/21 p=0.048
vs toms748 total 1385 vs 2216 per problem 41/6/19 p=0.0062
== IN-SAMPLE overlaps (13, for reference)
base total 142 solved 13/13 violations 0
A total 153 solved 13/13 violations 0
B total 154 solved 13/13 violations 0
chandrupatla total 135 solved 13/13 violations 0
brent total 128 solved 13/13 violations 0
toms748 total 151 solved 13/13 violations 0
A: R1 ✗ (153 vs 135) R2 ✗ (4/2/7 p=0.55) R3 ✓ (viol 0, solved 13 vs 13)
vs brent total 153 vs 128 per problem 4/1/8 p=0.39
vs toms748 total 153 vs 151 per problem 8/2/3 p=0.23
B: R1 ✗ (154 vs 135) R2 ✗ (3/0/10 p=0.092) R3 ✓ (viol 0, solved 13 vs 13)
vs brent total 154 vs 128 per problem 3/0/10 p=0.092
vs toms748 total 154 vs 151 per problem 5/4/4 p=1
PER PROBLEM, out-of-sample (A / B / Chandrupatla / Brent / TOMS748), * = unsolved:
f01: 8 / 10 / 3 / 10 / 9
f02: 12 / 12 / 10 / 13 / 10
f03: 12 / 42 / 12 / 12 / 17
f04: 9 / 9 / 9 / 10 / 11
f07: 10 / 13 / 11 / 12 / 11
f09: 10 / 9 / 10 / 10 / 11
f10: 10 / 10 / 10 / 9 / 8
f11: 11 / 10 / 10 / 9 / 7
f16: 15 / 10 / 8 / 7 / 9
f21: 10 / 9 / 9 / 10 / 10
f22: 8 / 9 / 10 / 10 / 10
f23: 9 / 9 / 10 / 10 / 10
f24: 26 / 26 / 43 / 122 / 88
f25: 27 / 27 / 43 / 106 / 76
f26: 26 / 26 / 41 / 121 / 95
f27: 17 / 25 / 14 / 32 / 25
f28: 21 / 21 / 47 / 119 / 73
f29: 16 / 16 / 12 / 30 / 25
f30: 17 / 17 / 12 / 13 / 14
f31: 5 / 13 / 13 / 12 / 18
f32: 41 / 11 / 12 / 13 / 14
f33: 17 / 20 / 12 / 14 / 13
f34: 9 / 9 / 10 / 9 / 10
f35: 20 / 22 / 16 / 11 / 15
f36: 49 / 52 / 47 / 39 / 47
f37: 19 / 19 / 17 / 31 / 29
f38: 51 / 48 / 47 / 47 / 51
f39: 59 / 58 / 47 / 73 / 97
f40: 51 / 47 / 47 / 49 / 77
f42: 9 / 9 / 11 / 10 / 10
f43: 25 / 25 / 44 / 106 / 91
f44: 30 / 30 / 44 / 104 / 106
f45: 43 / 43 / 44 / 117 / 123
f46: 14 / 15 / 14 / 15 / 19
f47: 14 / 13 / 15 / 15 / 18
f48: 14 / 19 / 17 / 16 / 15
f49: 13 / 13 / 10 / 11 / 11
f50: 10 / 13 / 10 / 12 / 13
f51: 9 / 9 / 9 / 10 / 10
f52: 18 / 16 / 14 / 17 / 22
f53: 11 / 11 / 12 / 13 / 11
f54: 7 / 7 / 7 / 8 / 9
f55: 8 / 10 / 9 / 11 / 9
f56: 9 / 10 / 9 / 11 / 10
f57: 11 / 11 / 11 / 12 / 16
f58: 8 / 9 / 10 / 10 / 10
f59: 12 / 10 / 9 / 13 / 13
f60: 7 / 7 / 8 / 8 / 8
f61: 10 / 12 / 11 / 11 / 11
f63: 9 / 11 / 10 / 10 / 10
f64: 8 / 8 / 9 / 9 / 9
f65: 8 / 8 / 9 / 9 / 9
f66: 14 / 13 / 12 / 10 / 13
f67: 11 / 11 / 12 / 12 / 12
f68: 7 / 8 / 9 / 8 / 8
f69: 8 / 8 / 10 / 10 / 11
f70: 10 / 10 / 12 / 11 / 13
f71: 5 / 13 / 11 / 13 / 16
f72: 29 / 25 / 48 / 110 / 112
f73: 26 / 26 / 43 / 120 / 91
f74: 26 / 26 / 43 / 122 / 91
f75: 13 / 18 / 27 / 66 / 61
f76: 44 / 44 / 43 / 43 / 43
f77: 51 / 43 / 43 / 46 / 66
f78: 48 / 48 / 43 / 44 / 45
f79: 47 / 43 / 40 / 40 / 39
f80: 23 / 27 / 29 / 21 / 21
f81: 57 / 44 / 50 / 45 / 39
f82: 4 / 4 / 5 / 4 / 5
f83: 32 / 25 / 48 / 106 / 76
f84: 8 / 8 / 13 / 8 / 19
f85: 14 / 53 / 15 / 12 / 13
f86: 19 / 21 / 13 / 16 / 17
f87: 5 / 33 / 11 / 12 / 14
f88: 15 / 15 / 12 / 13 / 13
f89: 16 / 14 / 14 / 14 / 19
f90: 16 / 15 / 12 / 15 / 14
f91: 14 / 14 / 10 / 13 / 15
rootsjl done