From 5c0550a0de12fb44cbbc930db10bb6d1c5695a68 Mon Sep 17 00:00:00 2001 From: Valeri Sitnikov Date: Tue, 22 Sep 2026 09:40:25 +0100 Subject: [PATCH] Open release of A' under the Apache License 2.0: LICENSE (verbatim Apache-2.0 text), NOTICE, licence stated in the paper's availability section and in simbracket's metadata. The next method is not described anywhere in the tree or in the history reachable from this branch. README no longer names the server. PDF rebuilt from the text as it stands. Server: verify 548 OK / 0 BAD, regression x2 1239 passed, PDF 32 pages, 0 errors, 0 overfull. Co-Authored-By: Claude Opus 5 --- LICENSE | 202 ++++++++++++++++++++++++++ NOTICE | 8 + article/sim_numerics.md | 2 +- article/sim_numerics.pdf | Bin 493931 -> 502562 bytes article/sim_numerics.tex | 307 +++++++++++++++++++++++++++------------ lib/setup.py | 1 + 6 files changed, 424 insertions(+), 96 deletions(-) create mode 100644 LICENSE create mode 100644 NOTICE diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..d645695 --- /dev/null +++ b/LICENSE @@ -0,0 +1,202 @@ + + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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We also recommend that a + file or class name and description of purpose be included on the + same "printed page" as the copyright notice for easier + identification within third-party archives. + + Copyright [yyyy] [name of copyright owner] + + Licensed under the Apache License, Version 2.0 (the "License"); + you may not use this file except in compliance with the License. + You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + + Unless required by applicable law or agreed to in writing, software + distributed under the License is distributed on an "AS IS" BASIS, + WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + See the License for the specific language governing permissions and + limitations under the License. diff --git a/NOTICE b/NOTICE new file mode 100644 index 0000000..08d67f4 --- /dev/null +++ b/NOTICE @@ -0,0 +1,8 @@ +sim-numerics — Root Finding by Similarity and Analogy +Copyright 2026 Valeri Sitnikov + +Licensed under the Apache License, Version 2.0 (see LICENSE). + +This product includes the proposed bracketing method A′, its reference implementation (simroot), +the compiled library simbracket, the benchmark harness, the problem corpora and every results file +behind the paper. diff --git a/article/sim_numerics.md b/article/sim_numerics.md index 012ec9c..f5354a7 100644 --- a/article/sim_numerics.md +++ b/article/sim_numerics.md @@ -558,7 +558,7 @@ The second is the steep flank. Where the loss remains — `fun9`, the near-cance ## Code and data availability -Everything behind this paper is released with it: the reference implementation of the base rule and of A′ (`simroot/pure.py`); `simbracket`, a compiled library of A′ (Cython; wheels for Linux and Windows, Python 3.10 or later) whose results equal the reference bit for bit on all 868 problems of the six corpora; the corpora as code (`corpus_*.py`); every sweep script with its results file; the advance records with the commits of Appendix D; and `verify_article.py`, which recomputes or re-reads every number stated in this paper and is part of the test suite. All numbers come from one Linux machine (§4). Repository: ⟨repository URL⟩. +Everything behind this paper is released with it: the reference implementation of the base rule and of A′ (`simroot/pure.py`); `simbracket`, a compiled library of A′ (Cython; wheels for Linux and Windows, Python 3.10 or later) whose results equal the reference bit for bit on all 868 problems of the six corpora; the corpora as code (`corpus_*.py`); every sweep script with its results file; the advance records with the commits of Appendix D; and `verify_article.py`, which recomputes or re-reads every number stated in this paper and is part of the test suite. All of it is released under the Apache License 2.0. All numbers come from one Linux machine (§4). 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a similarity rule --- the step -grows with how dissimilar \(f(x)\) is to the target 0, under a -similarity \(S\) with \(S(0)=1\) --- and derive its contraction factor -in closed form. The derivation fixes a base rule before any benchmark is -consulted: with the tent similarity and a three-point divided-difference -scale it is a Newton step of Muller's order 1.839, clipped to the -bracket and projected onto a budget of twice bisection whose multiplier -is its one numerical constant. On the 154 problems of Alefeld, Potra and -Shi it is level with TOMS 748 and 1.5\% behind Chandrupatla's method; on -wide brackets it is clearly behind. The gap is a decision, when to give -the model up, and we take it by analogy: at a flat root the -dimensionless configuration of the last three points recurs under zoom, -at a simple root it tends to a line, and the analogous pair gives the -order that says whether and where to split. This decision layer, about -ten discrete rules selected on two development sets, gives the method -A′. On 240 problems fixed before its code was frozen it needs 3656 -evaluations against 5717 for Chandrupatla, 5535 for ModAB and 4488 with -Lagouanelle's multiplicity estimate in place of the analogy; the lead -lies in multiple and fractional roots, present in two of the six -families. With the multiplicity known, the classical transformation +grows with the dissimilarity of \(f(x)\) to 0 under a similarity \(S\) +--- and derive its contraction factor in closed form. It fixes, before +any benchmark, a base rule: with the tent similarity and a three-point +divided-difference scale it is a Newton step of Muller's order 1.839, +clipped to the bracket and projected onto a budget of twice bisection +whose multiplier is its one numerical constant. On the 154 problems of +Alefeld, Potra and Shi it is level with TOMS 748 and 1.5\% behind +Chandrupatla's method; on wide brackets it is clearly behind. The gap is +a decision, when to give the model up, and we take it by analogy: at a +flat root the dimensionless configuration of the last three points +recurs under zoom, at a simple root it tends to a line, and the +analogous pair gives the order that says whether and where to split. +This decision layer --- about ten discrete rules selected on two +development sets --- gives A′. On 240 problems fixed before its code was +frozen it needs 3656 evaluations against 5717 for Chandrupatla, 5535 for +ModAB and 4488 with Lagouanelle's multiplicity estimate in place of the +analogy; the lead lies in multiple and fractional roots, present in two +of six families. With the multiplicity known, the transformation \(\operatorname{sign}(f)|f|^{1/m}\) is 2.4 to 6.8 times cheaper on -multiple roots. +multiple roots; A′ adds an estimate of the order, within a guarantee of +twice bisection. \end{abstract} \hypertarget{introduction}{% @@ -162,8 +162,8 @@ The paper makes four claims, each measured. The search that produced these results --- readings of the similarity that did not pay, the decomposition of the wide-bracket gap, wall-clock time, and the rejected rules --- is reported in Appendices A--C. The -code, the corpora and the pre-registrations are released (Appendix D and -the availability statement). +code, the corpora and the documents that recorded each test before its +run are released (Appendix D and the availability statement). \begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} @@ -400,8 +400,10 @@ while |B - A| > xtol: if sigma is 0 or not finite: xn <- midpoint(A,B) else: xn <- x + min(1, |f(x)|/sigma) * (far - x) # the step, eq (4) + lo, hi <- min(A,B), max(A,B) xn <- clamp(xn, hi - allow, lo + allow) # projection, eq (3) if xn outside (A,B) or already evaluated: xn <- midpoint(A,B) + (if the midpoint too was evaluated: return it) evaluate fn = f(xn); allow <- allow / 2 xp2, xp, x <- xp, x, xn update the bracket: whichever of A,B keeps the sign change @@ -554,15 +556,17 @@ transcribed by hand. it reports convergence and \(f\) changes sign within \(10^{-6}\) of the returned point, or vanishes there --- the bracketing notion of a root, the same criterion on every corpus of this paper; \(x\)-tolerance -\(10^{-12}\); budget 200 evaluations. Scoring against the published root -instead, as the benchmarks' harness does, charges every method the full -budget on six problems where \(f\) vanishes identically around the root -in floating point (§A.5). Head-to-head counts (wins/ties/losses) are -taken over every problem of a set with the same charging as the totals. -\emph{Failures are charged the full budget}, so no method can buy a low -total by giving up early, and totals are reported over all problems -rather than over the subset a method happened to solve. Rankings are by -failures first, then by total. +\(10^{-12}\); budget 200 evaluations. Every method, ours included, stops +when its bracket is no wider than \(\varepsilon_x\) or when it evaluates +an exact zero of the function it works on; none stops on a small +\(|f|\). Scoring against the published root instead, as the benchmarks' +harness does, charges every method the full budget on six problems where +\(f\) vanishes identically around the root in floating point (§A.5). +Head-to-head counts (wins/ties/losses) are taken over every problem of a +set with the same charging as the totals. \emph{Failures are charged the +full budget}, so no method can buy a low total by giving up early, and +totals are reported over all problems rather than over the subset a +method happened to solve. Rankings are by failures first, then by total. \textbf{Competitors.} Where SciPy ships the method, the competitor is the library --- Chandrupatla is @@ -655,7 +659,11 @@ its losses are the larger ones; by function family, the unit in which these problems are independent (§7), the comparison is 6/1/8 of 15 families, a tie. The constant-free variant goes 79/3/72 against Chandrupatla (\(p=0.63\)), 78/9/67 against TOMS 748 and 79/5/70 against -Brent. +Brent. Dekker, Illinois and false position fail \texttt{aps.13.00} under +either criterion and so keep their totals: they spend the whole budget +without converging, Dekker and Illinois stalled on one side of the zero +where \(|f|<10^{-62}\) but \(f\) does not change sign within +\(10^{-6}\). \textbf{Table 3.} Chandrupatla, 45 problems, brackets up to \(10^{12}\) wide, out of 264 configurations. @@ -689,7 +697,11 @@ total evals 2 & ITP, per-problem oracle & yes & 45/45 & 1675 & 0 \\ 3 & similarity, \(e^{-\lvert z\rvert}\), bracket scale, both guards & no & 45/45 & 1778 & 0 \\ +4 & similarity, \(e^{-\lvert z\rvert}\), bracket scale, bracket guard & +no & 45/45 & 1848 & 0 \\ 5 & ITP, recommended constants & yes & 45/45 & 1946 & 0 \\ +6 & similarity, \(e^{-\lvert z\rvert}\), bracket scale, earned +projection & no & 45/45 & 1952 & 0 \\ 9 & constant-free variant: earned projection & no & 45/45 & 2073 & 0 \\ 15 & bisection & no & 45/45 & 2136 & 0 \\ \textbf{49} & \textbf{base rule: tent, 3-point, projection (\(c=2\))} & @@ -774,8 +786,9 @@ the right move is to halve, Chandrupatla's method halves on up to all of its steps, and no reading of a single state measured takes that decision correctly. This section takes it by a similarity of the run to \emph{its own past} --- an analogy in Pólya's sense {[}8{]}, two situations -agreeing in more than one relation. Every rule below was pre-registered -with a stop rule (Appendix D); the rejected ones are in Appendix C. +agreeing in more than one relation. Every rule below was recorded, with +its criteria and stop rule, before its code and run (Appendix D); the +rejected ones are in Appendix C. \hypertarget{the-flag-a-promise-that-was-not-kept}{% \subsubsection{6.1 The flag: a promise that was not @@ -964,7 +977,10 @@ among the many candidates of Appendix C. That selection is why the method was tested once on a corpus fixed before its code was frozen, and against simpler rules put in its place (§7). Algorithm 2 is the complete method; \texttt{simroot/pure.py} and the compiled \texttt{simbracket} -implement exactly this and agree bit for bit. +implement exactly this and agree bit for bit. The nearest-configuration +search runs over the run's memory: \(O(n)\) per step, \(O(n^2)\) per run +of \(n\) evaluations (\(n\le200\) here), arithmetic that matters only +when \(f\) is cheap (Appendix B). \textbf{Algorithm 2 (A′).} Notation of Algorithm 1; \(S(z)=\max(0,1-|z|)\). @@ -987,9 +1003,11 @@ while |B - A| > xtol: # unkept promise, and unkept promise with a crossing flag <- not in_regime and last_model and fx/fp >= 1/4 flag_over <- not in_regime and last_model and fx/fp <= -1/4 - # order (6) of the analogous pair: the past configuration - # nearest to c (Euclidean in (xi, phi)), if nearer than the - # line phi = xi; inf if the pair shows L_f < 1 <= L_x; else none + # order (6) of the analogous pair. q <- the configuration in + # configs nearest to c (Euclidean in (xi, phi)); no m if c or + # configs is empty or q is not nearer than the line phi = xi. + # L_x <- |x-xp| / q.dx, L_f <- |fx-fp| / q.df + # m <- inf if L_f < 1 <= L_x (translation), else ln L_f / ln L_x m <- order of the analogous pair if m >= 2: analogy_seen <- true; m_a <- m if 0 < m <= 2/3: shallow_seen <- true; m_s <- m @@ -1003,18 +1021,20 @@ while |B - A| > xtol: else: step <- (1 - S(z)) * (far - x) # eq. (4) append x - xp to moves - # step pattern: the lag 2 .. half the history of highest - # mean similarity of successive length ratios has mean > 1/2, - # and step and x - xp point the same way - if the pattern repeats: + # step pattern: q_j <- |d_j|/|d_(j-1)| over the + # successive nonzero moves d (k ratios); + # rho(u,v) <- min(u,v)/max(u,v); repeats iff + # max_{p=2..floor(k/2)} mean_j rho(q_j, q_(j-p)) > 1/2 + if repeats and step, x - xp point the same way: s <- min(|step|,|x-xp|) / max(|step|,|x-xp|) step <- step / (1 - s), at most |far - x| long if |step| < xtol/2 and last_model and |fx/fp| < 1/4: step <- sign(far - x) * xtol/2 # tolerance step xn <- x + step; model <- true + lo, hi <- min(A,B), max(A,B) xn <- clamp(xn, hi - allow, lo + allow) # projection (3) if xn outside (A,B) or xn in {x, xp}: - xn <- mid; if mid in {x, xp}: stop + xn <- mid; if mid in {x, xp}: return mid last_model <- model and xn is the model's own point fn <- f(xn) if in_regime: # exit @@ -1056,8 +1076,8 @@ A′ per problem, CHA \endlastfoot \textbf{A′ (proposed)} & \textbf{2259} & \textbf{1074} & \textbf{3333} & --- & --- \\ -A′, earned budget (no free constant) & 3417 & 1852 & 5269 & & \\ -base rule (§3) & 2634 & 2357 & 4991 & & \\ +A′, earned budget (no free constant) & 3417 & 1852 & 5269 & --- & --- \\ +base rule (§3) & 2634 & 2357 & 4991 & --- & --- \\ Chandrupatla & 2595 & 1505 & 4100 & 103/20/31, \(p=3\cdot10^{-10}\) & 31/4/10, \(p=0.001\) \\ TOMS 748 & 2636 & 3088 & 5724 & 127/6/21 & 42/2/1 \\ @@ -1126,8 +1146,8 @@ sign contradiction & +11 & −12 & +29 & 0 & +1 & −1 & +28 \\ Every component is positive in sum; the regime and the split carry the method. The step pattern (earns on two corpora of six) and the sign contradiction (+28 over 855 problems) are marginal --- together under -one per cent, 117 of 13032 evaluations --- and are kept because the -pre-registered rule removes only a component that earns nowhere. +one per cent, 117 of 13032 evaluations --- and are kept because the rule +recorded in advance removes only a component that earns nowhere. \textbf{Table 7.} The similarity in the step of A′: the same method with each of the nine similarity functions of §5.2 in place of the tent, @@ -1220,22 +1240,25 @@ Roots.jl's \texttt{Order1B} and \texttt{Order2B} {[}12{]}); inside a bracket, {[}22{]} needs the multiplicity given and recognises a multiple root only by the number of evaluations spent, against a third of bisection's; Chandrupatla takes the decision to halve by an empirical -acceptance band {[}3{]}. §7.1 puts this claim against the detectors a -reader would try first, and against the transformation with the -multiplicity known in advance. +acceptance band {[}3{]}. §7.1 tests this against the detectors a reader +would try first and against the classical transformation with the +multiplicity known or estimated, and the outcome is sharper than the +claim: the order read by analogy transfers to the classical frame and +works better there than in A′'s own split, while A′'s exit is what keeps +simple roots cheap. \begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} \hypertarget{out-of-sample-evidence}{% \subsection{7. Out-of-sample evidence}\label{out-of-sample-evidence}} -Every decision above was taken on the two sets of §4. Pre-registration -protects each decision but not the chain: the final configuration --- a -decision layer of about ten discrete rules, chosen among the many -candidates listed in Appendix C --- was selected on the same 199 -problems. Four further corpora were therefore used, each fixed and -committed before any method was run on it, each with its criteria and -stop rule written down first. +Every decision above was taken on the two sets of §4. Recording each +decision in advance protects the decision but not the chain: the final +configuration --- a decision layer of about ten discrete rules, chosen +among the many candidates listed in Appendix C --- was selected on the +same 199 problems. Four further corpora were therefore used, each fixed +and committed before any method was run on it, each with its criteria +and stop rule written down first. \begin{enumerate} \def\labelenumi{\arabic{enumi}.} @@ -1279,8 +1302,8 @@ counting of every other method. The criterion, tolerance, budget and charging are those of §4. The variant carried to corpora 1--3 was A′ without the tolerance step -and the overshoot branch. It transferred to corpus 1 by every -pre-registered criterion (per problem 105/34/67 against Chandrupatla, +and the overshoot branch. It transferred to corpus 1 by every criterion +recorded in advance (per problem 105/34/67 against Chandrupatla, \(p=0.005\)), did \emph{not} transfer to Roots.jl (38/10/30, \(p=0.4\)) and lost on the applied corpus; the two readings that closed those gaps were developed on the seen corpora and tested once, on corpus 4. @@ -1426,8 +1449,8 @@ advance}\label{controls-simpler-detectors-and-the-multiplicity-known-in-advance} Two controls ask whether the gain of §6 comes from the recognition by analogy or only from the split (7) with any reasonable detector. Both -were pre-registered, with what the paper would say under every outcome, -before the run (\texttt{sweep\_controls.py}). +were recorded, with what the paper would say under every outcome, before +the run (\texttt{sweep\_controls.py}). \textbf{Other detectors in A′.} A′ is run with only its detector swapped; the memory, the split, the exit and the five readings of §6.4 @@ -1483,7 +1506,7 @@ none & 2693 & 2526 & 6165 & 20749 & 113/87/40 & \(3\cdot10^{-9}\) \\ \end{longtable} On corpus 4, the one test, A′ beats all three in total and problem by -problem, as the pre-registered criterion required. The competent +problem, as the criterion recorded in advance required. The competent alternative is Lagouanelle's estimate: it is slightly better on the canonical set (2235 against 2259), and on corpus 4 A′'s lead over it lies in the multiple-root and fractional-power families (1163 against @@ -1538,15 +1561,102 @@ corpus 4 & 88 & 2159 & 901 & 844 & 4151 \\ \end{longtable} With the multiplicity known the transformation is 2.4 to 6.8 times -cheaper than A′. A′ is far ahead of Chandrupatla on \(f\) itself, which -does not know the multiplicity either. On the remaining problems the -transformed and untransformed runs differ little and A′ is close to -them: ahead on the canonical sets (2259 against 2640, 420 against 437 -for Chandrupatla on \(g\)), behind on corpora 1 and 4 (2061 against -1924, 1497 against 1427). So on multiple roots the contribution of A′ is -the estimate of the order without knowing it, and the gap to Table 11 is -the price of that estimate --- large, and the clearest direction for -improving the method. +cheaper than A′. Every method, A′ included, stops on an exact zero of +the function it evaluates, and on the pure powers of the Chandrupatla +set \(g\) is exactly linear, so the secant lands on the root: 15 of +Brent's 20 runs and 4 of Chandrupatla's end that way there (A′: 2). On +new corpus 1 no transformed run ends on a zero, and the transformation +is still 3.4 times cheaper. A′ is far ahead of Chandrupatla on \(f\) +itself, which does not know the multiplicity either. On the remaining +problems the transformed and untransformed runs differ little and A′ is +close to them: ahead on the canonical sets (2259 against 2640, 420 +against 437 for Chandrupatla on \(g\)), behind on corpora 1 and 4 (2061 +against 1924, 1497 against 1427). So on multiple roots the contribution +of A′ is the estimate of the order without knowing it, and the gap to +Table 11 is the price of that estimate --- large, and the clearest +direction for improving the method. + +\textbf{The multiplicity estimated during the run.} Between A′ and the +oracle lies the natural classical method: Chandrupatla's interpolation +on \(g=\operatorname{sign}(f)|f|^{1/\hat m}\) with \(\hat m\) estimated +during the run. Our implementation of Chandrupatla's method (identical +to the library on all 199 problems, and to itself when +\(\hat m\equiv1\)) keeps the true \(f\) at its three points and reads +\(G(v)=\operatorname{sign}(v)|v|^{1/\hat m}\) only in the acceptance +band and the interpolation; \(\hat m\) starts at 1 and takes an order +read from the last three evaluations whenever that order lies on a +branch of §6.1 (\(m\ge2\) or \(0{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2000}} + >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2000}} + >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2000}} + >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2000}} + >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.2000}}@{}} +\toprule\noalign{} +\begin{minipage}[b]{\linewidth}\raggedright +method +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright +corpus 4 +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright +six corpora +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright +multiple/fractional (148) +\end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright +APS +\end{minipage} \\ +\midrule\noalign{} +\endhead +\bottomrule\noalign{} +\endlastfoot +\textbf{A′} & \textbf{3656} & \textbf{13032} & 4042 & \textbf{2259} \\ +Chandrupatla on \(g\), \(\hat m\) by analogy & 3806 & 15733 & 2809 & +3453 \\ +Chandrupatla on \(g\), \(\hat m\) by Lagouanelle & 7526 & 30991 & 6041 & +7215 \\ +the same, branch \(m\ge2\) only (post hoc) & 5568 & 18372 & 6540 & +2960 \\ +Chandrupatla on \(g\), \(m^*\) known (Table 11) & --- & --- & +\textbf{1355} & --- \\ +Chandrupatla on \(f\) & 5717 & 16481 & 7011 & 2595 \\ +\end{longtable} + +A′ is ahead of both estimated forms on corpus 4, in total and problem by +problem (against the analogy form 126/38/76, \(p=5\cdot10^{-4}\)), and +over the six corpora. The two estimators behave differently in this +frame. Lagouanelle's reads the parabola through Chandrupatla's points, +which alternate sides of the root; there it reports a fractional order +on 115 of the 154 simple roots of the canonical set, holds it, and turns +the method into little more than bisection. Restricted after the fact to +the branch \(m\ge2\) (post hoc, +\texttt{POSTHOC\_lag\_branch\_2026-09-22.md}), it no longer breaks, but +in this frame it hardly sees a multiple root either: 6540 on the 148 +multiple and fractional roots against 7011 for Chandrupatla on \(f\), +and 5568 on corpus 4, with A′ ahead 178/34/28. The analogy's order is +the better one here too, and on the multiple and fractional roots it +does better inside Chandrupatla's interpolation than inside A′'s split: +it closes 59\%, 58\% and 31\% of the gap from A′ to the oracle on the +Chandrupatla set, corpus 1 and corpus 4 (322 against 654, 721 against +1229, 1766 against 2159). It pays on simple roots, where it has no exit +to take a false reading back (3453 against 2595 on the canonical set). +Two conclusions follow. First, the order read by analogy transfers to +the classical frame and works better there than in A′'s own split: on +the multiple and fractional roots Chandrupatla's interpolation with that +order beats A′ itself (2809 against 4042). Second, A′'s decision layer +as a whole --- the detector together with its exit --- earns its place: +without an exit the transferred detector loses more on simple roots than +it gains on multiple ones, and A′ stays ahead on corpus 4 and over the +six corpora. \begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} @@ -1574,9 +1684,12 @@ translation, a simple root tends to the line, and the analogous pair reads the order that decides between the model and a split. The method built on it, A′, is ahead of Chandrupatla on both canonical sets, and on a corpus fixed before its code was frozen it needs 36\% fewer -evaluations and wins 177 problems to 28. Its decision layer beats -Lagouanelle's estimate, Chandrupatla's band and no detector put in its -place; with the multiplicity known in advance the classical +evaluations and wins 177 problems to 28. Its detector, the order read by +analogy, beats Lagouanelle's estimate, Chandrupatla's band and no +detector put in its place, and it transfers: inside Chandrupatla's +interpolation on the transformed function it does better on multiple +roots than A′'s own split, while only A′'s exit keeps simple roots +cheap; with the multiplicity known in advance the classical transformation is 2.4 to 6.8 times cheaper on multiple roots, which measures what estimating the order costs. The claim the measurements support is a lead over Brent, TOMS 748, ITP and ModAB everywhere, within @@ -1592,9 +1705,7 @@ behind or level. The first is the price of estimating the order. With the multiplicity given, the transformation of §6.3 is 2.4 to 6.8 times cheaper than A′ on -multiple and fractional roots (Table 11): the order read from the -analogous pair, or its use in the split, loses most of what the -transformation could deliver. +multiple and fractional roots (Table 11): closing that gap is open. The second is the steep flank. Where the loss remains --- \texttt{fun9}, the near-cancelling class, 4 − tan x at its pole --- the base step @@ -1616,10 +1727,11 @@ implementation of the base rule and of A′ (\texttt{simroot/pure.py}); and Windows, Python 3.10 or later) whose results equal the reference bit for bit on all 868 problems of the six corpora; the corpora as code (\texttt{corpus\_*.py}); every sweep script with its results file; the -pre-registrations with the commits of Appendix D; and +advance records with the commits of Appendix D; and \texttt{verify\_article.py}, which recomputes or re-reads every number -stated in this paper and is part of the test suite. All numbers come -from one Linux machine (§4). Repository: ⟨repository URL⟩. +stated in this paper and is part of the test suite. All of it is +released under the Apache License 2.0. All numbers come from one Linux +machine (§4). Repository: ⟨repository URL⟩. \begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} @@ -2254,17 +2366,17 @@ results}\label{appendix-c.-negative-results}} \textbf{The decision reading ``defect'' does not transfer.} Combined with the regime it was the best configuration on the two development sets (§A.4's defect reading with the flat families of §6), and it - passed every pre-registered criterion there. On new corpus 1 it did + passed every criterion recorded for it there. On new corpus 1 it did not: per problem 95/33/78 against Chandrupatla (\(p=0.22\)), losing the class of exponential flanks 9 to 26. It is therefore not part of A′. \item \textbf{A component rejected alone can pay in combination.} - Remembering the analogy for the run was rejected by its own - pre-registration, under the harness scoring of the time (canonical set - 2814 against 2806 without the regime; under the sign-change criterion - the two are level, 2633 against 2634), and with the split of §6.3 it - is the better form (with the step pattern, wide brackets 1250 against + Remembering the analogy for the run was rejected by its own advance + record, under the harness scoring of the time (canonical set 2814 + against 2806 without the regime; under the sign-change criterion the + two are level, 2633 against 2634), and with the split of §6.3 it is + the better form (with the step pattern, wide brackets 1250 against 1388 for the analogy read in one state). Composition was measured, not assumed, throughout --- which is also why §A.2's readings (2) and (3), each an improvement, are not combined. @@ -2272,9 +2384,9 @@ results}\label{appendix-c.-negative-results}} \begin{center}\rule{0.5\linewidth}{0.5pt}\end{center} -\hypertarget{appendix-d.-pre-registrations-and-the-frozen-code}{% -\subsection{Appendix D. Pre-registrations and the frozen -code}\label{appendix-d.-pre-registrations-and-the-frozen-code}} +\hypertarget{appendix-d.-advance-records-and-the-frozen-code}{% +\subsection{Appendix D. Advance records and the frozen +code}\label{appendix-d.-advance-records-and-the-frozen-code}} Every rule of §6 and every test of §7 was written down, with its criteria and stop rule, before its code and its run. Table D1 gives, for @@ -2282,12 +2394,17 @@ each document, the commit that first added it and the commit that first added the results its run wrote, both read from git by \texttt{check\_prereg\_order.py}: 25 of the 30 were committed before their results; four were committed together with them, so git cannot -order them; one was decided on its smoke run and has no results file. -The code of A′ was committed (\texttt{8027d7f}) after corpus 4 was -defined (\texttt{657df10}) and before its results (\texttt{6d2531e}); -\texttt{simroot/pure.py} did not change in between. +order them; one was decided on its smoke run and has no results file. We +call these documents advance records, not pre-registrations: they live +in the author's repository, and their order relative to the runs is +attested only by the author's git history, whose timestamps the author +sets; no external registry was used. A deposit with an external +timestamp (Zenodo, OSF) before a run would remove that limitation for +future tests. The code of A′ was committed (\texttt{8027d7f}) after +corpus 4 was defined (\texttt{657df10}) and before its results +(\texttt{6d2531e}); \texttt{simroot/pure.py} did not change in between. -\textbf{Table D1.} Pre-registrations, in the order they were written. +\textbf{Table D1.} Advance records, in the order they were written. \begin{longtable}[]{@{} >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.3030}} @@ -2297,7 +2414,7 @@ defined (\texttt{657df10}) and before its results (\texttt{6d2531e}); >{\raggedright\arraybackslash}p{(\columnwidth - 8\tabcolsep) * \real{0.1313}}@{}} \toprule\noalign{} \begin{minipage}[b]{\linewidth}\raggedright -pre-registration +advance record \end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright commit \end{minipage} & \begin{minipage}[b]{\linewidth}\raggedright diff --git a/lib/setup.py b/lib/setup.py index d6dcb6f..f734db5 100644 --- a/lib/setup.py +++ b/lib/setup.py @@ -36,6 +36,7 @@ setup( name="simbracket", version="1.0.0", description="Bracketing root finding by similarity and analogy (compiled).", + license="Apache-2.0", packages=["simbracket"], package_data={}, include_package_data=False,