PolynomialErrorOptimization.jl fits polynomials against a combined objective:

• approximation error,
• modeled finite-precision evaluation error.

The recommended entry point is:

using PolynomialErrorOptimization

approx = approxfit(sin, (-2.0, 2.0); target = 1e-8)

@show error_bound(approx)
@show coeff_count(approx)
@show approx(0.25)

• Stable workflow layer: approxfit, fit_abs, fit_rel, recommend_parameters, Approximation, error_bound, coeff_count, is_piecewise, pieces, and the built-in scheme builders.
• Expert layer: fixed-degree drivers, piecewise drivers, search strategies, and standalone evaluator generation.
• Internal or research layer: exchange substeps, symbolic error-expression nodes, and low-level row/basis machinery.

If you are starting fresh, stay in the stable workflow layer until you need explicit control over degree policy, search, or evaluation-scheme construction.

This package is not registered yet. From Julia:

using Pkg
Pkg.develop(path = "/path/to/PolynomialErrorOptimization")
Pkg.instantiate()

• docs/src/index.md: landing page and package overview.
• docs/src/high-level-interface.md: recommended workflow.
• docs/src/choosing-a-workflow.md: decision guide for single vs piecewise, absolute vs relative, and degree vs budget.
• docs/src/examples.md: practical recipes.
• docs/src/technical-guide.md: internals and extension points.
• docs/src/contributor-guide.md: contributor workflow and redesign roadmap.
• docs/src/api.md: API split by stability layer.

Run tests from the package root with:

using Pkg
Pkg.test()

Build the docs locally with:

julia --project=docs docs/make.jl

If you use the package, cite the underlying paper by Arzelier, Bréhard, Hubrecht, and Joldeș:

@article{ArzelierBrehardHubrechtJoldes2025,
    author  = {Arzelier, Denis and Br{\'e}hard, Florent and Hubrecht, Tom and Jolde\c{s}, Mioara},
    title   = {An Exchange Algorithm for Optimizing both Approximation and
                         Finite-Precision Evaluation Errors in Polynomial Approximations},
    journal = {ACM Trans. Math. Softw.},
    year    = {2025},
    doi     = {10.1145/3770066}
}

This implementation is provided as-is for research/educational purposes; users should consult the original paper and the upstream Sollya-based reference implementation at https://gitlab.laas.fr/mmjoldes/xatom for production use.