In the ideal world, we describe our models with recognizable mathematical expressions and directly evaluate those models over large data samples with high performance. Numerical backends from the Machine Learning community, such as JAX, Pytorch and TensorFlow, already take a lot of work from our shoulders with their out-of-the-box support for multithreading, GPUs, and autodiff. But it turns out that we can bring the code even closer to physics by inserting a Computer Algebra System.
[The ComPWA project](https://compwa-org.rtfd.io) formulates amplitude models symbolically with SymPy. These symbolic expressions not only make it easy for the user to inspect the physics that is implemented, but can also serve as a template to high-performance numerical backends like NumPy, JAX and Numba. As such, the CAS provides a self-documenting, single-source of truth for the physics that is implemented and gives us the means to quickly switch between different computational backends. In addition, the CAS analytically simplifies the expressions, which in some instances results in a small performance boost.