Root Finding by Similarity and Analogy — code, data and history
Companion archive to the paper Root Finding by Similarity and Analogy: A Bracketing Method with a Data-Selected Decision Layer (V. Sitnikov). Everything behind the paper is here, under the Apache License 2.0: the method's reference implementation, a compiled library of the proposed method A′, the benchmark harness, the problem corpora, every results file, the records written before each run, the paper itself, and the full development history.
Contents
| path | what |
|---|---|
source/ |
the repository at the commit the paper was built from: simroot/ (the reference implementation of the base rule, A′ and every variant the paper measures), lib/ (the source of the compiled library simbracket), the sweep scripts, corpora (corpus_*.py), diagnoses, the verifier verify_article.py, the tests, every results file (sweep_*.json, results_*.txt), the records written before the runs (PREREG_*.md, POSTHOC_*.md), the findings (FINDINGS_*.md) and the paper (article/) |
sim-numerics.bundle |
the full git history of that branch (git clone sim-numerics.bundle); the commits cited in the paper's Appendix D are in it |
wheels/ |
simbracket, A′ as a compiled library (Python ≥ 3.10; Linux and Windows builds) |
requirements.txt, reproduce.sh |
the Python packages used, and the one-command reproduction |
SHA256SUMS |
checksums of every file in the archive |
Requirements
Linux x86_64 for reproducing the numbers. The paper's numbers come from one Linux machine (Ubuntu
24.04, glibc 2.39, Python 3.12.3). The test functions call the platform's libm, whose last digit
differs between platforms; on Windows, TOMS 748 needs 2635 evaluations on the Alefeld–Potra–Shi set
instead of 2636, and two of the paper's fresh recomputations move by a few evaluations. Using the
method needs no particular platform.
Reproduce
./reproduce.sh
creates a virtual environment, installs requirements.txt and the simbracket wheel, and in source/
runs
python -u verify_article.py— recomputes or re-reads every number stated in the paper (548) and compares it with the value printed there; it ends with every number stated in the paper matches the sweep data;python -m pytest tests/test_simbracket_equivalence.py— the compiled library equals the reference implementation bit for bit, point and evaluation count, on all 868 problems of the six corpora.
Any table can be recomputed from scratch with its sweep script; each script's docstring names the table
it produces (for example python -u rescore_uniform.py for the protocol tables, python -u sweep_fourth.py --fourth for corpus 4, python -u sweep_controls.py and python -u sweep_estimated.py
for the controls). The full test suite is python -m pytest tests.
Use A′ on your own problem
from simbracket import find_root, evaluation_bound
x, nfev, converged = find_root(f, a, b, xtol=1e-12, maxfev=200)
# f(a) and f(b) of opposite signs; stops when the bracket is no wider than xtol or f(x) == 0;
# never more than evaluation_bound(a, b, xtol) = 2*ceil(log2(|b-a|/xtol)) + 3 evaluations
or, from source, simroot.pure.pure_root with the configuration named APRIME in sweep_full.py.
The records and their order
PREREG_*.md were written, and committed, before the runs they describe; POSTHOC_*.md after, as
marked. Appendix D of the paper lists each record with its commit and the commit of its results;
check_prereg_order.py recomputes that table from the history in sim-numerics.bundle. The order is
attested by the author's git history, not by an external registry. Before publication the history was
rewritten once to remove infrastructure details (a server address); the commit hashes cited in the paper
are those of the rewritten history in this archive.
Citing
The archive: https://doi.org/10.5281/zenodo.22894337 (DOI 10.5281/zenodo.22894337). Please cite the paper together with it.
Licence
Apache License 2.0 (LICENSE); copyright Valeri Sitnikov (NOTICE).