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.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

sweep_rootsjl.py

@@ -0,0 +1,104 @@
+"""PREREG_roots_jl_2026-09-21: variants A, B, the plain rule and the three library rivals on
+the Roots.jl / ModAB bracketing benchmark (corpus_roots_jl.py).
+
+    python -u sweep_rootsjl.py            run -> sweep_rootsjl.json, then the verdicts
+    python -u sweep_rootsjl.py --report   verdicts only
+"""
+from __future__ import annotations
+
+import json
+import math
+import sys
+from multiprocessing import Pool
+
+from corpus_roots_jl import build, solved
+from sweep_full import MAXFEV, XTOL, make_method
+from sweep_oos import CONFIGS as OOS_CONFIGS
+from sweep_oos import sign_p
+
+NAMES = ("base", "A", "B", "chandrupatla", "brent", "toms748")
+
+
+def evaluate(name):
+    method = make_method(OOS_CONFIGS[name])
+    probs, _ = build()
+    res = {}
+    for pid, f, a, b, ins in probs:
+        try:
+            x, n, conv = method(f, a, b, XTOL, MAXFEV)
+            x = float(x)
+        except Exception:
+            x, n, conv = float("nan"), MAXFEV, False
+        ok = bool(conv and solved(f, x))
+        over = ok and int(n) > 2 * math.ceil(math.log2(abs(b - a) / XTOL)) + 4
+        res[pid] = [int(n), ok, bool(over), bool(ins)]
+    return name, res
+
+
+def cost(v):
+    return v[0] if v[1] else MAXFEV
+
+
+def report(R):
+    keep_main = lambda pid, v: not v[3]
+    keep_strict = lambda pid, v: not v[3] and int(pid[1:]) >= 24
+    keep_ins = lambda pid, v: v[3]
+    ch = R["chandrupatla"]
+    for title, keep in (("MAIN (78 out-of-sample)", keep_main),
+                        ("STRICT (f24-f91, out-of-sample)", keep_strict),
+                        ("IN-SAMPLE overlaps (13, for reference)", keep_ins)):
+        print(f"\n== {title}")
+        for k in NAMES:
+            r = R[k]
+            sel = {p: v for p, v in r.items() if keep(p, v)}
+            print(f"  {k:<14} total {sum(cost(v) for v in sel.values()):6d}  "
+                  f"solved {sum(v[1] for v in sel.values()):3d}/{len(sel)}  "
+                  f"violations {sum(v[2] for v in sel.values())}")
+        for v_name in ("A", "B"):
+            r = R[v_name]
+            sel = [p for p, v in r.items() if keep(p, v)]
+            tot = sum(cost(r[p]) for p in sel)
+            tot_ch = sum(cost(ch[p]) for p in sel)
+            w = sum(cost(r[p]) < cost(ch[p]) for p in sel)
+            l = sum(cost(r[p]) > cost(ch[p]) for p in sel)
+            t = len(sel) - w - l
+            viol = sum(r[p][2] for p in sel)
+            sv, sc = sum(r[p][1] for p in sel), sum(ch[p][1] for p in sel)
+            r1, r2, r3 = tot < tot_ch, w > l and sign_p(w, l) < 0.05, viol == 0 and sv >= sc
+            line = (f"  {v_name}: R1 {'✓' if r1 else '✗'} ({tot} vs {tot_ch})  R2 {'✓' if r2 else '✗'} "
+                    f"({w}/{t}/{l} p={sign_p(w, l):.2g})  R3 {'✓' if r3 else '✗'} (viol {viol}, "
+                    f"solved {sv} vs {sc})")
+            if keep is keep_main:
+                line += "  -> " + ("TRANSFERS" if r1 and r2 and r3 else "does NOT transfer")
+            print(line)
+            for rn in ("brent", "toms748"):
+                o = R[rn]
+                w2 = sum(cost(r[p]) < cost(o[p]) for p in sel)
+                l2 = sum(cost(r[p]) > cost(o[p]) for p in sel)
+                print(f"       vs {rn:<8} total {tot} vs {sum(cost(o[p]) for p in sel)}  "
+                      f"per problem {w2}/{len(sel) - w2 - l2}/{l2} p={sign_p(w2, l2):.2g}")
+    print("\nPER PROBLEM, out-of-sample (A / B / Chandrupatla / Brent / TOMS748), * = unsolved:")
+    for p, v in R["A"].items():
+        if v[3]:
+            continue
+        cells = []
+        for k in ("A", "B", "chandrupatla", "brent", "toms748"):
+            c = R[k][p]
+            cells.append(f"{c[0]}{'' if c[1] else '*'}")
+        print(f"  {p}: " + " / ".join(cells))
+
+
+def main():
+    if "--report" not in sys.argv:
+        with Pool(len(NAMES)) as pool:
+            R = dict(pool.map(evaluate, NAMES))
+        with open("sweep_rootsjl.json", "w", encoding="utf8") as fh:
+            json.dump(R, fh)
+    with open("sweep_rootsjl.json", encoding="utf8") as fh:
+        R = json.load(fh)
+    report(R)
+    print("rootsjl done")
+
+
+if __name__ == "__main__":
+    main()