chasing Chandrupatla found a property of the BENCHMARK: on all five fun7 problems f vanishes identically near the declared root (f(0+t)=0 up to 3.2e-2), every method stops at a point where f(x)=0 exactly and is scored a failure by the |x-root|<=1e-6 rule — so 1000 evaluations of EVERY wide-bracket total are an artefact and the universal '40 of 45' is a scoring statement. Re-scored: 45/45 for everyone but Brent, ranking unchanged, gap to Chandrupatla 253 (17%) and diffuse across 8 families. Written into the paper with its reproducing scripts; pdflatex clean, verifier green

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

diag_fun7_root.py

@@ -0,0 +1,57 @@
+"""Is fun7 a method failure or a SCORING failure?
+
+Every method stops on fun7 within 8-22 evaluations and every one is scored unsolved. This
+checks the only thing that matters: is f actually zero at the point each method returned?
+If it is, the methods found a root and the benchmark's |x - declared_root| <= 1e-6 check is
+what fails — 5 of the 45 problems then contribute 200 dead evaluations each to EVERY
+method's total, which is a fact about the scoring, not about the methods.
+
+    python -u diag_fun7_root.py
+"""
+
+from __future__ import annotations
+
+import inspect
+import math
+
+from scipy.optimize._tstutils import _CHANDRUPATLA_TESTS_DICTS
+
+from simroot.baselines import best_of, chandrupatla, chandrupatla_scipy
+from simroot.pure import pure_root
+from sweep_full import MAXFEV, XTOL
+
+CHA = best_of(chandrupatla, chandrupatla_scipy)
+
+
+def main():
+    for d in _CHANDRUPATLA_TESTS_DICTS:
+        if not str(d["ID"]).startswith("fun7"):
+            continue
+        f, root = d["f"], float(d["root"])
+        a, b = (float(v) for v in d["bracket"])
+        x_o, n_o, _ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio",
+                                  scale="derived3", guard="safe", prestep="slope",
+                                  direction="dissimilar")
+        x_c, n_c, _okc = CHA(f, a, b, XTOL, MAXFEV)
+        print(f"{d['ID']:<8} declared root {root:+.3g}")
+        for nm, x, n in (("ours", x_o, n_o), ("chandrupatla", float(x_c), n_c)):
+            fx = f(x)
+            print(f"   {nm:<13} returned x={x:+.10g} after {n:3d} evals  "
+                  f"f(x)={fx:+.3e}  |x-root|={abs(x - root):.3g}  "
+                  f"{'f IS ZERO THERE' if fx == 0.0 else 'f is not zero'}")
+        # how wide is the flat zero region around the declared root?
+        w = 0.0
+        for k in range(0, 40):
+            t = 10.0 ** (-12 + k * 0.5)
+            if f(root + t) == 0.0:
+                w = t
+            else:
+                break
+        print(f"   f is identically zero at least up to root + {w:.3g}")
+    src = inspect.getsource(_CHANDRUPATLA_TESTS_DICTS[0]["f"]) if False else None
+    if src:
+        print(src)
+
+
+if __name__ == "__main__":
+    main()