vvsandClaude Opus 5
99be33a632
X5: dissimilar+slope with A reaches 2859+2545 = 5404 over both sets, the best total this line has measured (was 5511; Chandrupatla 5228) - but again by trading the canonical set (2726 -> 2859) for the wide brackets (2785 -> 2545). The one-step replay (APS no harm) did not carry over: its bracket-halving metric rewards overshooting the root, which on a simple root costs superlinear convergence in the full run - the declared one-step limitation, now measured. Among the nine functions A helps only the tent (6026 -> 5892) and slightly ratio_soft. Also: pin 'strictly fewer evaluations on every flat problem' was wrong for 6(x-2)^5 on [0,10] - both runs are budget-bound (90 of the guaranteed 91); corrected to the measured claim. verify_article 286/286, 836 tests pass twice. Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
79 lines
3.1 KiB
Python
79 lines
3.1 KiB
Python
"""Pins for PREREG_extrapolate_in_method_2026-09-21.md: step extrapolation (A)."""
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from __future__ import annotations
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import math
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import pytest
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from simroot.pure import pure_root
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SMOOTH = (
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(lambda t: t ** 3 - 2.0 * t - 5.0, 1.0, 4.0),
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(lambda t: math.exp(t) - 2.0, 0.0, 3.0),
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(lambda t: math.sin(t) - 0.5, 0.0, 1.5),
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)
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FLAT = (
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(lambda t: 6.0 * (t - 2.0) ** 5, 0.0, 10.0),
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(lambda t: t ** 9, -1.0, 2.0),
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(lambda t: (t - 3.0) ** 3, 0.0, 10.0),
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)
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XTOL, MAXFEV = 1e-12, 200
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@pytest.mark.parametrize("f,a,b", SMOOTH + FLAT)
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@pytest.mark.parametrize("guard", ("project", "safe", "credit"))
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def test_default_is_the_published_method_bit_for_bit(f, a, b, guard):
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ref = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard=guard)
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off = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard=guard,
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extrapolate="none")
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assert ref == off
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@pytest.mark.parametrize("f,a,b", SMOOTH + FLAT)
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@pytest.mark.parametrize("guard", ("project", "credit"))
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def test_the_guarantee_survives_extrapolation(f, a, b, guard):
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x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard=guard, extrapolate="steps")
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assert ok and min(a, b) <= x <= max(a, b)
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half = math.ceil(math.log2(abs(b - a) / XTOL))
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bound = 2 * half + 3 if guard == "project" else half + 4
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assert n <= bound, (n, bound)
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@pytest.mark.parametrize("f,a,b", FLAT[1:])
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def test_extrapolation_breaks_the_flat_cycle(f, a, b):
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"""The mechanism the pre-registration rests on: on a pure power the similar successive
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undershoots are replaced by a longer step, and the run gets cheaper."""
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_x, n_off, _ = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard="project")
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_x, n_on, _ = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard="project", extrapolate="steps")
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assert n_on < n_off, (n_on, n_off)
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def test_on_a_budget_bound_run_extrapolation_changes_the_path_not_the_count():
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"""MEASURED, pinned as measured: on 6(x-2)^5 over [0, 10] both runs cost 90 evaluations
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against a projection guarantee of 2*44 + 3 = 91 - the budget schedule, not the step,
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decides when the run ends. The paths differ from the fourth evaluation on (87
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positions), so the mode is active; its gain is absorbed by the safeguard here. The
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expectation written first (strictly fewer evaluations) was wrong for this problem."""
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f, a, b = FLAT[0]
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ev = {}
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for mode in ("none", "steps"):
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seen = []
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def g(t, _s=seen):
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_s.append(t)
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return f(t)
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_x, n, ok = pure_root(g, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3",
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guard="project", extrapolate=mode)
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assert ok
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ev[mode] = (n, seen)
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assert ev["steps"][0] <= ev["none"][0]
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assert ev["steps"][1] != ev["none"][1]
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def test_unknown_mode_is_refused():
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with pytest.raises(ValueError):
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pure_root(lambda t: t, -1.0, 1.0, XTOL, MAXFEV, extrapolate="aitken")
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