Gorgonia is a library that helps facilitate machine learning in Go.

Math.NET Numerics

automatic differentiation made easier for C++

Open-source cross-platform symbolic algebra library for C# and F#. Can be used for both production and research purposes.

Transparent calculations with uncertainties on the quantities involved (aka "error propagation"); calculation of derivatives.

a symbolic math expression evaluator for javascript

clad -- automatic differentiation for C/C++

Single cell trajectory detection

An interface to various automatic differentiation backends in Julia.

Source Code Generation for Automatic Differentiation using Operator Overloading

A simple cross platform .NET API for Intel MKL

FastAD is a C++ implementation of automatic differentiation both forward and reverse mode.

Deep.Net machine learning framework for F#

Modern Fortran Numerical Differentiation Library

➗ Library for parsing math expressions with rational numbers, finding their derivatives and compiling an optimal IL code

Optimal numerical differentiation of noisy time series data in python.

xFunc provides a powerful parser and analyzer for mathematical expressions. It excels at calculating derivatives, simplifying expressions, and achieving high performance.

Backpropagate derivatives through the Cholesky decomposition

Numerical derivatives for Python

Pattern matching language for transforming complex tree-structured data (strings, XML, JSON, algebraic expressions). Built-in symbolic algebra, backtracking, and exact arithmetic. Portable C99.