We present a machine learning algorithm that generates symbolic hyperelasticity models optimized for fast and robust inference in 3D Eulerian hydrocodes. Unlike classical deep learning methods, which require large neural networks that may hinder inference speed, the proposed algorithm converts neural network models into compact symbolic representations, balancing expressivity and execution. By projecting strain data onto a hyperplane and employing neural additive models with univariate bases, we facilitate efficient symbolic regression via genetic programming. This approach explicitly controls the trade-off between model accuracy and computational speed, making it ideal for high-fidelity hydrocodes requiring rapid material point evaluations. The availability of analytical solutions further enables interpretation of the learned models.