diff --git a/analyze_extrap.py b/analyze_extrap.py new file mode 100644 index 0000000..68961fe --- /dev/null +++ b/analyze_extrap.py @@ -0,0 +1,100 @@ +"""Verdicts X1-X5 of PREREG_extrapolate_in_method_2026-09-21.md from sweep_extrap.json. + + python -u analyze_extrap.py +""" +from __future__ import annotations + +import json +import math + +FLAT = ("fun3", "fun4", "fun5", "fun6") +FAMILY = ("project", "safe", "credit") + + +def load(p): + with open(p, encoding="utf8") as fh: + return json.load(fh) + + +def key(r): + s = r["spec"] + return (s[1], s[2], s[3], s[5], s[6], s[7]) + + +def fam_sum(r, fams): + return sum((n if ok else 200) for pid, (n, ok) in r["CHA"]["per"].items() + if pid.split(".")[0] in fams) + + +def sign_p(w, l): + k, n = min(w, l), w + l + return min(1.0, 2.0 * sum(math.comb(n, i) for i in range(k + 1)) / 2.0 ** n) if n else 1.0 + + +def h2h(a, b, s): + w = t = l = 0 + for pid, (na, oka) in a[s]["per"].items(): + nb, okb = b[s]["per"][pid] + if oka and okb: + w += na < nb + l += na > nb + t += na == nb + return w, t, l + + +def main(): + rows = load("sweep_extrap.json") + full = {r["label"]: r for r in load("sweep_full.json")} + cha = full["chandrupatla"] + pairs = {} + for r in rows: + pairs.setdefault(key(r), {})[r["spec"][9]] = r + readings = {("none", "recent", "distance"): "plain", ("slope", "recent", "distance"): "slope", + ("slope", "shape", "distance"): "shape+slope", + ("slope", "recent", "dissimilar"): "dissim+slope", + ("defect", "recent", "distance"): "defect"} + print("tent, three-point, pairs (without A -> with A): APS | CHA | both | flat fun3-6 sum") + for (sim, sc, gu, pre, pts, dirn), p in sorted(pairs.items()): + if sim != "ratio" or gu not in FAMILY + ("none",): + continue + a, b = p["none"], p["steps"] + rd = readings[(pre, pts, dirn)] + print(f" {rd:<13} {gu:<8} {a['APS']['total']:5d}->{b['APS']['total']:<5d} " + f"{a['CHA']['total']:5d}->{b['CHA']['total']:<5d} " + f"{a['APS']['total'] + a['CHA']['total']:5d}->" + f"{b['APS']['total'] + b['CHA']['total']:<5d} " + f"{fam_sum(a, FLAT):4d}->{fam_sum(b, FLAT):<4d} " + f"solved {b['APS']['solved'] + b['CHA']['solved']} over {b['APS']['over'] + b['CHA']['over']}") + prop = pairs[("ratio", "derived3", "project", "none", "recent", "distance")] + a, b = prop["none"], prop["steps"] + print("\nVERDICTS for the proposed rule (tent, 3-point, projection)") + print(f" X1 CHA < 3220: {b['CHA']['total']} -> {'PASS' if b['CHA']['total'] < 3220 else 'FAIL'}") + print(f" X2 APS <= 2806: {b['APS']['total']} -> {'PASS' if b['APS']['total'] <= 2806 else 'FAIL'}") + fam = [p["steps"] for k, p in pairs.items() if k[2] in FAMILY] + viol = sum(r["APS"]["over"] + r["CHA"]["over"] for r in fam) + low = [r["label"] for r in fam if r["APS"]["solved"] + r["CHA"]["solved"] < 193] + print(f" X3 guarantee family with A: {viol} violations over {len(fam)} cells; " + f"cells solving < 193: {len(low)} -> {'PASS' if viol == 0 and not low else 'FAIL'}") + fa, fb = fam_sum(a, FLAT), fam_sum(b, FLAT) + print(f" X4 flat fun3-6 sum: {fa} -> {fb} -> {'PASS' if fb < fa else 'FAIL'}") + best = min((p["steps"] for p in pairs.values() + if p["steps"]["spec"][3] in FAMILY + and p["steps"]["APS"]["solved"] + p["steps"]["CHA"]["solved"] >= 193), + key=lambda r: r["APS"]["total"] + r["CHA"]["total"]) + print(f" X5 best pair with A over both sets: {best['label']} " + f"{best['APS']['total']}+{best['CHA']['total']}=" + f"{best['APS']['total'] + best['CHA']['total']} (reference 5511, Chandrupatla 5228)") + for s in ("APS", "CHA"): + w, t, l = h2h(b, cha, s) + print(f" proposed + A vs Chandrupatla, {s}: {w}/{t}/{l} sign p={sign_p(w, l):.2g} " + f"totals {b[s]['total']} vs {cha[s]['total']}") + print("\nnine functions, three-point, projection, no readings (without A -> with A), both sets:") + for (sim, sc, gu, pre, pts, dirn), p in sorted(pairs.items()): + if gu == "project" and pre == "none" and pts == "recent" and dirn == "distance": + a2, b2 = p["none"], p["steps"] + print(f" {sim:<11} {a2['APS']['total'] + a2['CHA']['total']:6d} -> " + f"{b2['APS']['total'] + b2['CHA']['total']:6d}") + + +if __name__ == "__main__": + main() diff --git a/results_analyze_extrap.txt b/results_analyze_extrap.txt new file mode 100644 index 0000000..d32d57d --- /dev/null +++ b/results_analyze_extrap.txt @@ -0,0 +1,41 @@ +tent, three-point, pairs (without A -> with A): APS | CHA | both | flat fun3-6 sum + defect credit 3545->4134 2949->2926 6494->7060 1044->993 solved 193 over 0 + plain credit 3568->4130 3020->2986 6588->7116 1044->988 solved 193 over 0 + dissim+slope credit 3857->4223 3002->2947 6859->7170 1043->1002 solved 193 over 0 + slope credit 3507->4121 2997->3007 6504->7128 1051->1007 solved 193 over 0 + shape+slope credit 3755->4169 3021->3059 6776->7228 1064->1064 solved 193 over 0 + defect none 2523->3180 4198->3508 6721->6688 2806->2081 solved 188 over 1 + plain none 2806->2967 4104->3471 6910->6438 2707->2070 solved 188 over 0 + dissim+slope none 2726->2859 2785->2545 5511->5404 1376->1157 solved 193 over 0 + slope none 2848->2971 3075->2735 5923->5706 1710->1331 solved 193 over 0 + shape+slope none 2675->2930 5443->5452 8118->8382 4000->4000 solved 173 over 0 + defect project 2523->3180 3210->2954 5733->6134 1818->1527 solved 193 over 0 + plain project 2806->2967 3220->2925 6026->5892 1823->1524 solved 193 over 0 + dissim+slope project 2726->2859 2785->2545 5511->5404 1376->1157 solved 193 over 0 + slope project 2848->2971 3074->2735 5922->5706 1709->1331 solved 193 over 0 + shape+slope project 2675->2930 3498->3506 6173->6436 2055->2054 solved 193 over 0 + defect safe 3131->3207 3368->3386 6499->6593 1943->1929 solved 193 over 0 + plain safe 3036->3171 3363->3389 6399->6560 1950->1931 solved 193 over 0 + dissim+slope safe 3123->3170 2683->2710 5806->5880 1228->1248 solved 193 over 0 + slope safe 3020->3187 2903->2895 5923->6082 1484->1469 solved 193 over 0 + shape+slope safe 2527->2986 3108->3223 5635->6209 1629->1687 solved 193 over 0 + +VERDICTS for the proposed rule (tent, 3-point, projection) + X1 CHA < 3220: 2925 -> PASS + X2 APS <= 2806: 2967 -> FAIL + X3 guarantee family with A: 0 violations over 39 cells; cells solving < 193: 0 -> PASS + X4 flat fun3-6 sum: 1823 -> 1524 -> PASS + X5 best pair with A over both sets: pure+dissim+ext+slope.ratio.derived3.project 2859+2545=5404 (reference 5511, Chandrupatla 5228) + proposed + A vs Chandrupatla, APS: 42/62/49 sign p=0.53 totals 2967 vs 2787 + proposed + A vs Chandrupatla, CHA: 11/1/28 sign p=0.0095 totals 2925 vs 2441 + +nine functions, three-point, projection, no readings (without A -> with A), both sets: + cbrt 17993 -> 18181 + cosine 19784 -> 19753 + exp_abs 6652 -> 6869 + exp_sq 19786 -> 19780 + rat_sq 19793 -> 19796 + ratio 6026 -> 5892 + ratio_soft 9352 -> 9285 + rational 6823 -> 7483 + sqrt 13381 -> 13633 diff --git a/simroot/pure.py b/simroot/pure.py index e528975..498dc75 100644 --- a/simroot/pure.py +++ b/simroot/pure.py @@ -542,7 +542,8 @@ def _local_order(x2, f2, x1, f1, x0, f0): def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", guard="step", stats=None, budget_factor=2.0, budget_extra=None, endowment=1.0, space="x", prestep="none", - points="recent", direction="distance", exponent="none"): + points="recent", direction="distance", exponent="none", + extrapolate="none"): """The pure similarity root finder. similarity : key into PURE_SIMS @@ -594,6 +595,8 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", if scale not in ("derived", "derived3", "derived_rho", "derived3_rho", "derived3_m", "derived3_cap", "start", "bracket", "far"): raise ValueError(f"unknown scale {scale!r}") + if extrapolate not in ("none", "steps"): + raise ValueError(f"unknown extrapolate {extrapolate!r}") if exponent not in EXPONENTS: raise ValueError(f"unknown exponent {exponent!r}") if exponent == "order" and scale not in ("derived3", "derived3_cap", "bracket", "far"): @@ -863,6 +866,26 @@ def pure_root(f, a, b, xtol, maxfev, similarity="ratio", scale="derived", step = _log_space_step(S, x, fx, far, slope, c_near, xtol) if step is None: step = (1.0 - S(z_now)) * (far - x) + if extrapolate == "steps": + # PREREG 2026-09-21 (A in the method). The similarity of THIS + # step to the previous displacement: two successive moves the + # same way, of similar length, mean the iterate creeps along a + # geometric series whose remainder is step*S/(1-S) - so the + # step is lengthened by 1/(1-S). On x^m under a Newton step + # S = 1 - 1/m and the factor is m, which lands on the root. + # At a simple root successive steps shrink superlinearly, S -> + # 0 and the step is untouched. Capped at the far end, the same + # bound the step itself has; no constant. + d_prev = x - x_prev + if (step != 0.0 and d_prev != 0.0 + and (step > 0.0) == (d_prev > 0.0)): + s_steps = (min(abs(step), abs(d_prev)) + / max(abs(step), abs(d_prev))) + if s_steps < 1.0: + longer = step / (1.0 - s_steps) + reach = abs(far - x) + step = (longer if abs(longer) <= reach + else math.copysign(reach, step)) if stats is not None and "trace" in stats: # DIAGNOSTIC HOOK, behaviour-neutral: records the state each # step was taken from, so another model can be evaluated on the diff --git a/sweep_extrap.json b/sweep_extrap.json new file mode 100644 index 0000000..37df539 --- /dev/null +++ b/sweep_extrap.json @@ -0,0 +1 @@ +[{"label": "pure+dissim+ext+slope.ratio.derived3.none", "spec": ["pure", "ratio", "derived3", "none", "x", "slope", "recent", "dissimilar", "none", "steps"], "APS": {"total": 2859, "solved": 153, "n": 154, "over": 0, "per": {"aps.01.00": [11, true], "aps.02.00": [32, true], "aps.02.01": [24, true], "aps.02.02": [15, true], "aps.02.03": [23, true], "aps.02.04": [35, true], "aps.02.05": [42, true], "aps.02.06": [43, true], "aps.02.07": [33, true], "aps.02.08": [28, true], "aps.02.09": [25, true], "aps.03.00": [17, true], "aps.03.01": [39, true], "aps.03.02": [35, true], "aps.04.00": [29, true], "aps.04.01": [41, true], "aps.04.02": [13, true], "aps.04.03": [14, true], "aps.04.04": [18, true], "aps.04.05": [14, true], "aps.04.06": [14, true], "aps.04.07": [14, true], "aps.04.08": [14, true], "aps.04.09": [13, true], "aps.04.10": [13, true], "aps.04.11": [15, true], "aps.04.12": [16, true], "aps.04.13": [16, true], "aps.05.00": [9, true], "aps.06.00": [8, true], "aps.06.01": [8, true], "aps.06.02": [9, true], "aps.06.03": [10, true], "aps.06.04": [10, true], "aps.06.05": [11, true], "aps.06.06": [10, true], "aps.06.07": [10, true], "aps.06.08": [14, true], "aps.06.09": [14, true], "aps.07.00": [12, true], "aps.07.01": [13, true], "aps.07.02": [15, true], "aps.08.00": [3, true], "aps.08.01": [10, true], "aps.08.02": [13, true], "aps.08.03": [12, true], "aps.08.04": [11, true], "aps.09.00": [10, true], "aps.09.01": [10, true], "aps.09.02": [13, true], "aps.09.03": [14, true], "aps.09.04": [18, true], "aps.09.05": [21, true], "aps.09.06": [22, true], "aps.10.00": [19, true], "aps.10.01": [27, true], "aps.10.02": [30, true], "aps.10.03": [31, true], "aps.10.04": [11, true], "aps.11.00": [9, true], "aps.11.01": [12, true], "aps.11.02": [15, true], "aps.11.03": [14, true], "aps.12.00": [10, true], "aps.12.01": [11, true], "aps.12.02": [12, true], "aps.12.03": [12, true], "aps.12.04": [12, true], "aps.12.05": [12, true], "aps.12.06": [11, true], "aps.12.07": [12, true], "aps.12.08": [10, true], "aps.12.09": [9, true], "aps.12.10": [10, true], "aps.12.11": [10, true], "aps.12.12": [10, true], "aps.12.13": [11, true], "aps.12.14": [10, true], "aps.12.15": [10, true], "aps.12.16": [10, true], "aps.12.17": [9, true], "aps.12.18": [9, true], "aps.13.00": [10, false], "aps.14.00": [15, true], "aps.14.01": [15, true], "aps.14.02": [15, true], "aps.14.03": [15, true], "aps.14.04": [15, true], "aps.14.05": [15, true], "aps.14.06": [15, true], "aps.14.07": [15, true], "aps.14.08": [15, true], "aps.14.09": [15, true], "aps.14.10": [15, true], "aps.14.11": [15, true], "aps.14.12": [15, true], "aps.14.13": [15, true], "aps.14.14": [15, true], "aps.14.15": [15, true], "aps.14.16": [15, true], "aps.14.17": [15, true], "aps.14.18": [15, true], "aps.14.19": [15, true], "aps.14.20": [15, true], "aps.14.21": [15, true], "aps.14.22": [15, true], "aps.14.23": [15, true], "aps.14.24": [15, true], "aps.14.25": [15, true], "aps.14.26": [15, true], "aps.14.27": [15, true], "aps.14.28": [15, true], "aps.14.29": [15, true], "aps.14.30": [15, true], "aps.14.31": [15, true], "aps.14.32": [15, true], "aps.14.33": [15, true], "aps.14.34": [15, true], "aps.14.35": [15, true], "aps.14.36": [15, true], "aps.14.37": [15, true], "aps.14.38": [15, true], "aps.14.39": [15, true], "aps.15.00": [20, true], "aps.15.01": [21, true], "aps.15.02": [22, true], "aps.15.03": [22, true], "aps.15.04": [21, true], "aps.15.05": [21, true], "aps.15.06": [21, true], "aps.15.07": [21, true], "aps.15.08": [21, true], "aps.15.09": [21, true], "aps.15.10": [21, true], "aps.15.11": [21, true], "aps.15.12": [21, true], "aps.15.13": [22, true], "aps.15.14": [22, true], "aps.15.15": [22, true], "aps.15.16": [23, true], "aps.15.17": [23, true], "aps.15.18": [24, true], "aps.15.19": [23, true], "aps.15.20": [23, true], "aps.15.21": [25, true], "aps.15.22": [28, true], "aps.15.23": [27, true], "aps.15.24": [29, true], "aps.15.25": [26, true], "aps.15.26": [28, true], "aps.15.27": [29, true], "aps.15.28": [30, true], "aps.15.29": [29, true], "aps.15.30": [28, true]}}, "CHA": {"total": 2545, "solved": 40, "n": 45, "over": 0, "per": {"fun1.1": [16, true], "fun1.2": [12, true], "fun1.3": [16, true], "fun1.4": [30, true], "fun1.5": [44, true], "fun2.1": [10, true], "fun2.2": [26, true], "fun2.3": [15, true], "fun2.4": [45, true], "fun2.5": [49, true], "fun3.1": [56, true], "fun3.2": [56, true], "fun3.3": [36, true], "fun3.4": [36, true], "fun3.5": [83, true], "fun4.1": [58, true], "fun4.2": [60, true], "fun4.3": [61, true], "fun4.4": [69, true], "fun4.5": [88, true], "fun5.1": [60, true], "fun5.2": [51, true], "fun5.3": [52, true], "fun5.4": [57, true], "fun5.5": [58, true], "fun6.1": [58, true], "fun6.2": [55, true], "fun6.3": [52, true], "fun6.4": [54, true], "fun6.5": [57, true], "fun7.1": [10, false], "fun7.2": [11, false], "fun7.3": [12, false], "fun7.4": [11, false], "fun7.5": [13, false], "fun8.1": [10, true], "fun8.2": [10, true], "fun8.3": [12, true], "fun8.4": [12, true], "fun8.5": [11, true], "fun9.1": [10, true], "fun9.2": [11, true], "fun9.3": [15, true], "fun9.4": [17, true], "fun9.5": [17, true]}}}, {"label": "pure+ext.ratio.derived3.none", "spec": ["pure", "ratio", "derived3", "none", "x", "none", "recent", "distance", "none", "steps"], "APS": {"total": 2967, "solved": 153, "n": 154, "over": 0, "per": {"aps.01.00": [10, true], "aps.02.00": [10, true], "aps.02.01": [26, true], "aps.02.02": [28, true], "aps.02.03": [14, true], "aps.02.04": [17, true], "aps.02.05": [16, true], "aps.02.06": [13, true], "aps.02.07": [16, true], "aps.02.08": [17, true], "aps.02.09": [19, true], "aps.03.00": [19, true], "aps.03.01": [16, true], "aps.03.02": [16, true], "aps.04.00": [17, true], "aps.04.01": [44, true], "aps.04.02": [37, true], "aps.04.03": [18, true], "aps.04.04": [17, true], "aps.04.05": [14, true], "aps.04.06": [12, true], "aps.04.07": [13, true], "aps.04.08": [16, true], "aps.04.09": [15, true], "aps.04.10": [18, true], "aps.04.11": [12, true], "aps.04.12": [18, true], "aps.04.13": [18, true], "aps.05.00": [9, true], "aps.06.00": [8, true], "aps.06.01": [8, true], "aps.06.02": [9, true], "aps.06.03": [10, true], "aps.06.04": [10, true], "aps.06.05": [11, true], "aps.06.06": [10, true], "aps.06.07": [10, true], "aps.06.08": [14, true], "aps.06.09": [14, true], "aps.07.00": [12, true], "aps.07.01": [13, true], "aps.07.02": [15, true], "aps.08.00": [3, true], "aps.08.01": [10, true], "aps.08.02": [14, true], "aps.08.03": [12, true], "aps.08.04": [11, true], "aps.09.00": [10, true], "aps.09.01": [11, true], "aps.09.02": [13, true], "aps.09.03": [14, true], "aps.09.04": [18, true], "aps.09.05": [21, true], "aps.09.06": [22, true], "aps.10.00": [19, true], "aps.10.01": [12, true], "aps.10.02": [30, true], "aps.10.03": [17, true], "aps.10.04": [11, true], "aps.11.00": [9, true], "aps.11.01": [12, true], "aps.11.02": [17, true], "aps.11.03": [15, true], "aps.12.00": [9, true], "aps.12.01": [9, true], "aps.12.02": [10, true], "aps.12.03": [10, true], "aps.12.04": [10, true], "aps.12.05": [11, true], "aps.12.06": [11, true], "aps.12.07": [11, true], "aps.12.08": [10, true], "aps.12.09": [9, true], "aps.12.10": [10, true], "aps.12.11": [10, true], "aps.12.12": [10, true], "aps.12.13": [11, true], 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"fun2.2": [200, false], "fun2.3": [200, false], "fun2.4": [200, false], "fun2.5": [200, false], "fun3.1": [200, false], "fun3.2": [200, false], "fun3.3": [200, false], "fun3.4": [200, false], "fun3.5": [200, false], "fun4.1": [200, false], "fun4.2": [200, false], "fun4.3": [200, false], "fun4.4": [200, false], "fun4.5": [200, false], "fun5.1": [200, false], "fun5.2": [200, false], "fun5.3": [111, true], "fun5.4": [124, true], "fun5.5": [128, true], "fun6.1": [200, false], "fun6.2": [200, false], "fun6.3": [200, false], "fun6.4": [200, false], "fun6.5": [200, false], "fun7.1": [200, false], "fun7.2": [200, false], "fun7.3": [200, false], "fun7.4": [200, false], "fun7.5": [200, false], "fun8.1": [200, false], "fun8.2": [200, false], "fun8.3": [200, false], "fun8.4": [200, false], "fun8.5": [200, false], "fun9.1": [200, false], "fun9.2": [200, false], "fun9.3": [200, false], "fun9.4": [200, false], "fun9.5": [200, false]}}}] \ No newline at end of file diff --git a/sweep_full.py b/sweep_full.py index 7ee993a..70f05cd 100644 --- a/sweep_full.py +++ b/sweep_full.py @@ -85,10 +85,10 @@ def itp_oracle(f, a, b, xtol, maxfev): return best if best is not None else (0.5 * (a + b), maxfev, False) -# Competitors are taken at the better of SciPy's implementation and ours, -# problem by problem, wherever SciPy ships the method. Ours turned out to be -# the cheaper of the two - 6991 against brentq's 7004, 5209 against -# _chandrupatla's 5228 - so quoting the library alone would have flattered us. +# Competitors are the LIBRARY wherever SciPy ships the method (since 2026-09-21): +# Brent = brentq, Chandrupatla = elementwise.find_root. Until then they were the +# per-problem better of the library and ours, which let a tolerance slip in our +# Chandrupatla (a bracket twice as wide) leak into the reported numbers. BASELINES = { "bisection": bisection, "regula_falsi": regula_falsi, "illinois": illinois, "pegasus": pegasus, @@ -115,11 +115,13 @@ def make_method(spec): points = spec[6] if len(spec) > 6 else "recent" direction = spec[7] if len(spec) > 7 else "distance" exponent = spec[8] if len(spec) > 8 else "none" + extrapolate = spec[9] if len(spec) > 9 else "none" def m(f, a, b, xtol, maxfev): return pure_root(f, a, b, xtol, maxfev, similarity=sim, scale=scale, guard=guard, space=space, prestep=prestep, - points=points, direction=direction, exponent=exponent) + points=points, direction=direction, exponent=exponent, + extrapolate=extrapolate) return m @@ -133,6 +135,9 @@ def label(spec): tag = f"{tag}+shape" if len(spec) > 7 and spec[7] != "distance": tag = f"{tag}+dissim" + if len(spec) > 9 and spec[9] != "none": + # the pair (off, on) must be distinguishable in a results file + tag = f"{tag}+ext" if len(spec) > 8 and spec[8] != "none": # the exponent must be visible in the label: (far, none) is false position and # (far, order) is the hypothesis, and a results file that cannot tell them apart @@ -205,6 +210,39 @@ def build_grid_log(smoke): for sim in sims for sc in ("derived", "derived3") for gu in guards] +def _preflight_extrap_mode(): + """Fail LOUDLY if extrapolate is not deployed (see _preflight_log_mode).""" + x, _n, ok = pure_root(lambda t: t - 1.0, 0.0, 3.0, 1e-10, 100, similarity="ratio", + scale="derived3", guard="project", extrapolate="steps") + if not (ok and abs(x - 1.0) < 1e-8): + raise SystemExit("extrapolate preflight FAILED: refusing to report zeros") + + +def build_grid_extrap(smoke): + """PREREG 2026-09-21: step extrapolation (A) inside the method, every cell as a pair + (none, steps). Tent with every reading and every guard; all nine functions without + readings, so the law across the grid is visible with and without A.""" + _preflight_extrap_mode() + guards = ("project", "credit") if smoke else GUARD_MODES + readings = [("none", "recent", "distance")] if smoke else [ + ("none", "recent", "distance"), ("slope", "recent", "distance"), + ("slope", "shape", "distance"), ("slope", "recent", "dissimilar"), + ("defect", "recent", "distance")] + specs = [] + for gu in guards: + for pre, pts, dirn in readings: + for ex in ("none", "steps"): + specs.append(("pure", "ratio", "derived3", gu, "x", pre, pts, dirn, + "none", ex)) + sims = ["sqrt"] if smoke else [s for s in sorted(PURE_SIMS) if s != "ratio"] + for sim in sims: + for gu in guards: + for ex in ("none", "steps"): + specs.append(("pure", sim, "derived3", gu, "x", "none", "recent", + "distance", "none", ex)) + return specs + + def _preflight_decision_mode(): """Fail LOUDLY if the decision readings are not deployed (see _preflight_log_mode).""" for md in ("band", "defect", "simpair"): @@ -335,10 +373,12 @@ def main(): capmode = "--cap" in sys.argv # scale selected between the two computed ones ordermode = "--order" in sys.argv # slot 1: the similarity read BY PLACE decmode = "--decision" in sys.argv # slot 2: the reading in the DECISION place + extmode = "--extrap" in sys.argv # A in the method: step extrapolation combomode = "--combo" in sys.argv # modes A and B together pointsmode = "--points" in sys.argv # mode A: triple by shape dirmode = "--direction" in sys.argv # mode B: far end by dissimilarity - specs = (build_grid_decision(smoke) if decmode else + specs = (build_grid_extrap(smoke) if extmode else + build_grid_decision(smoke) if decmode else build_grid_order(smoke) if ordermode else build_grid_cap(smoke) if capmode else build_grid_combo(smoke) if combomode else @@ -362,8 +402,9 @@ def main(): # the published sweep_full.json is what verify_article.py checks the paper # against, so the log grid never writes into it - if decmode or ordermode or capmode or combomode or pointsmode or dirmode: - base = ("sweep_decision" if decmode else + if extmode or decmode or ordermode or capmode or combomode or pointsmode or dirmode: + base = ("sweep_extrap" if extmode else + "sweep_decision" if decmode else "sweep_order" if ordermode else "sweep_cap" if capmode else "sweep_combo" if combomode else diff --git a/tests/test_extrapolate.py b/tests/test_extrapolate.py new file mode 100644 index 0000000..839c3e4 --- /dev/null +++ b/tests/test_extrapolate.py @@ -0,0 +1,78 @@ +"""Pins for PREREG_extrapolate_in_method_2026-09-21.md: step extrapolation (A).""" +from __future__ import annotations + +import math + +import pytest + +from simroot.pure import pure_root + +SMOOTH = ( + (lambda t: t ** 3 - 2.0 * t - 5.0, 1.0, 4.0), + (lambda t: math.exp(t) - 2.0, 0.0, 3.0), + (lambda t: math.sin(t) - 0.5, 0.0, 1.5), +) +FLAT = ( + (lambda t: 6.0 * (t - 2.0) ** 5, 0.0, 10.0), + (lambda t: t ** 9, -1.0, 2.0), + (lambda t: (t - 3.0) ** 3, 0.0, 10.0), +) +XTOL, MAXFEV = 1e-12, 200 + + +@pytest.mark.parametrize("f,a,b", SMOOTH + FLAT) +@pytest.mark.parametrize("guard", ("project", "safe", "credit")) +def test_default_is_the_published_method_bit_for_bit(f, a, b, guard): + ref = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard=guard) + off = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", guard=guard, + extrapolate="none") + assert ref == off + + +@pytest.mark.parametrize("f,a,b", SMOOTH + FLAT) +@pytest.mark.parametrize("guard", ("project", "credit")) +def test_the_guarantee_survives_extrapolation(f, a, b, guard): + x, n, ok = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", + guard=guard, extrapolate="steps") + assert ok and min(a, b) <= x <= max(a, b) + half = math.ceil(math.log2(abs(b - a) / XTOL)) + bound = 2 * half + 3 if guard == "project" else half + 4 + assert n <= bound, (n, bound) + + +@pytest.mark.parametrize("f,a,b", FLAT[1:]) +def test_extrapolation_breaks_the_flat_cycle(f, a, b): + """The mechanism the pre-registration rests on: on a pure power the similar successive + undershoots are replaced by a longer step, and the run gets cheaper.""" + _x, n_off, _ = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", + guard="project") + _x, n_on, _ = pure_root(f, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", + guard="project", extrapolate="steps") + assert n_on < n_off, (n_on, n_off) + + +def test_on_a_budget_bound_run_extrapolation_changes_the_path_not_the_count(): + """MEASURED, pinned as measured: on 6(x-2)^5 over [0, 10] both runs cost 90 evaluations + against a projection guarantee of 2*44 + 3 = 91 - the budget schedule, not the step, + decides when the run ends. The paths differ from the fourth evaluation on (87 + positions), so the mode is active; its gain is absorbed by the safeguard here. The + expectation written first (strictly fewer evaluations) was wrong for this problem.""" + f, a, b = FLAT[0] + ev = {} + for mode in ("none", "steps"): + seen = [] + + def g(t, _s=seen): + _s.append(t) + return f(t) + _x, n, ok = pure_root(g, a, b, XTOL, MAXFEV, similarity="ratio", scale="derived3", + guard="project", extrapolate=mode) + assert ok + ev[mode] = (n, seen) + assert ev["steps"][0] <= ev["none"][0] + assert ev["steps"][1] != ev["none"][1] + + +def test_unknown_mode_is_refused(): + with pytest.raises(ValueError): + pure_root(lambda t: t, -1.0, 1.0, XTOL, MAXFEV, extrapolate="aitken")