Many common photonic states are so-called Gaussian states. In a recent manuscript, we have shown how the photon statistics of such states can be obtained by constructing and differentiating generating functions. In this technical report, we demonstrate the straightforward application of the framework PyTorch to compute the required multivariate higher-order derivatives by automatic differentiation. Its implementation requires only a few lines of Python code corroborating the strength of our approach based on generating functions for the computation of photon statistics.