# Paper on the accuracy of math functions

**URL:** https://discourse.julialang.org/t/paper-on-the-accuracy-of-math-functions/132227
**Category:** Numerics
**Tags:** juliamath, accuracy
**Created:** [September 9, 2025, 11:02am UTC](https://discourse.julialang.org/t/paper-on-the-accuracy-of-math-functions/132227 "2025-09-09T11:02:11Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![JeffreySarnoff](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jeffreysarnoff/32/1980_2.png) [@JeffreySarnoff](https://discourse.julialang.org/u/JeffreySarnoff)
#### Post date: [September 9, 2025, 11:02am UTC](https://discourse.julialang.org/t/paper-on-the-accuracy-of-math-functions/132227/1 "2025-09-09T11:02:12Z")

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Mantas Mikaitis and Tejaswa Rizyal have this well developed, reliable paper

> **[Accuracy of Mathematical Functions in Julia](https://arxiv.org/abs/2509.05666)**
>
> Basic computer arithmetic operations, such as $+$, $\\times$, or $÷$ are correctly rounded, whilst mathematical functions such as $e^x$, $\\ln(x)$, or $\\sin(x)$ in general are not, meaning that separate implementations may provide different results...

The software is available on github:

> **[GitHub - north-numerical-computing/MathBenchmark.jl: An easy to configure and deploy software package...](https://github.com/north-numerical-computing/MathBenchmark.jl)**
>
> An easy to configure and deploy software package for measuring the errors of mathematical functions in the Julia programming language.

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### Author: ![nsajko](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/nsajko/32/221187_2.png) [@nsajko](https://discourse.julialang.org/u/nsajko)
#### Post date: [February 1, 2026, 9:04pm UTC](https://discourse.julialang.org/t/paper-on-the-accuracy-of-math-functions/132227/2 "2026-02-01T21:04:20Z")

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Related: visualizations for functions discussed in the paper and more:

> [@Floating-point accuracy visualization example: the ULP error for each math function coming with Julia](https://discourse.julialang.org/t/new-on-forem-floating-point-accuracy-visualization-example-the-ulp-error-for-each-math-function-coming-with-julia/135392):
>
> Introduction The implementation of a math function, such as cos(::Float64) in Julia, should be fast, but also needs to be at least somewhat accurate. Here I propose a method for visualizing empirical accuracy data. Consider the discrepancy between the exact value of a univariate real function, such as the sine, and the approximate value that is returned by a call such as sin(0.3). By putting an interval that subsets the domain of the function on the x-axis of a plot, and the value of this discr…