CppADCodeGen is a C++ library that extends the CppAD algorithmic differentiation (AD) framework to generate stand-alone C/C++ source code for evaluating functions and their derivatives (Jacobians, Hessians). It converts a CppAD operation tape into a computation graph and then emits efficient, compilable code via multiple backends: C, LaTeX, MathML, and DOT. The generated code can be compiled into dynamic libraries at runtime (Linux) or JIT-compiled using Clang/LLVM, enabling high-performance derivative computation in production environments. The library also includes a suite of algorithms for differential-algebraic equation (DAE) index reduction (Pantelides, Soares-Secchi, dummy derivatives), pattern detection for loop optimization, sparse derivative computation, and a thread pool for parallel evaluation. It is heavily used in scientific computing, simulation, and optimization contexts (e.g., chemical engineering models). The codebase is a header-only template library with optional runtime compilation components, distributed under dual EPL-1.0 and GPL-3.0 licenses.
Algebrite is a symbolic mathematics library (Computer Algebra System) written in TypeScript. It provides a comprehensive set of operations including symbolic differentiation, integration, polynomial factorization, root finding, matrix/tensor algebra, arbitrary-precision arithmetic, and expression simplification. Internally, it uses an S-expression representation (Cons cells) and a recursive-descent parser to convert string expressions into algebraic trees. The library exposes both a string-based `run()` API for evaluating expressions and direct method calls (e.g., `Algebrite.factor`). It was originally forked from EigenMath and retains some CoffeeScript legacy in test files and debug logging. The codebase is large and monolithic, with many modules tightly coupled through shared global state (the `defs` object). Despite this, the implementation is functional and covers a wide range of mathematical operations, making it suitable for embedding in interactive notebooks or computational tools.