PREREG before code and run: both directions. (1) defect decision combined with the flat regime (analogy / remembered analogy) for canonical headroom; (2) contra: halve when the local secant's sign contradicts the bracket's - the fun9 cause (a near-cancelling left end, |f| doubling 17 steps in a row); traces: 3/5 fun9, 7/154 canonical, 0 flat. Composite prestep 'a+b+c', one per category; factorial grid on the proposed rule +/- G2; decided on the smoke; goal = below Chandrupatla on both; ablation of every component of the best cell.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
2026-09-21 15:45:03 +01:00
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+"""Why the proposed rule loses on fun9 (exp(x) - 2 - 0.01/x^2 + 2e-6/x^3, brackets from
+[2e-4, 1] to [2e-4, 81]) - and whether the cause is a distinguishing sign.
+
+On fun9.4 the two negative powers nearly cancel at the left end: f(2e-4) = -1 against
+5e11 at the right end, so the rule reads the root as near the left end, while f dives to
+-3.7e4 before it turns up to the root at 0.703.  17 model steps in a row DOUBLE |f|: the
+local slope has the sign opposite to the one the bracket demands (f must rise from its
+negative end to its positive end).
+
+The sign considered: the local secant of the last two points, (fx - fp)/(x - xp), against
+the bracket's, (FB - FA)/(B - A).  Opposite signs = the local picture contradicts the
+bracket.  Per state (trace hook, proposed rule, no regime) and per problem, per group.
+Nothing in the method changes.
+
+    python -u diag_fun9_slope_sign.py
+"""
+from __future__ import annotations
+
+from collections import defaultdict
+
+from simroot.pure import pure_root
+from sweep_full import MAXFEV, XTOL, load_problems
+
+FLAT = ("fun3", "fun4", "fun5", "fun6")
+
+
+def main():
+    per = defaultdict(lambda: [0, 0, 0, 0])   # problems, with any contradiction, states, contradicting
+    for s, pid, f, a, b, _root in load_problems():
+        st = {"trace": []}
+        pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
+                  guard="project", stats=st)
+        fam = pid.split(".")[0]
+        g = "APS" if s == "APS" else ("CHA-flat" if fam in FLAT else f"CHA-{fam}")
+        bad = 0
+        for t in st["trace"]:
+            if t["x"] == t["xp"]:
+                continue
+            loc = (t["fx"] - t["fp"]) / (t["x"] - t["xp"])
+            brk = (t["FB"] - t["FA"]) / (t["B"] - t["A"])
+            per[g][2] += 1
+            if loc != 0.0 and (loc > 0.0) != (brk > 0.0):
+                bad += 1
+        per[g][0] += 1
+        per[g][1] += bad > 0
+        per[g][3] += bad
+    print(f"{'group':<10} {'problems':>8} {'any contradiction':>18} {'states':>7} {'contradicting':>14}")
+    for g in sorted(per):
+        n, anyc, sts, c = per[g]
+        print(f"{g:<10} {n:8d} {anyc:18d} {sts:7d} {c:14d}")
+    print("diag done")
+
+
+if __name__ == "__main__":
+    main()