"""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()