The process of Big Bang Nucleosynthesis (BBN) is a crucial test of cosmology. In this talk, I will describe a new code for predicting the primordial elemental abundance due to BBN. This code takes advantage of JAX, a machine learning framework, to enable fast and differentiable predictions of elemental abundances. This allows us to put BBN calculations on the same level of rigor and ease-of-use as cosmic microwave background analyses, taking nuclear rate uncertainties fully into account. The differentiable nature of the code will also allow the use of more sophisticated and efficient methods of parameter estimation beyond e.g. traditional MCMC techniques.