jax-ml/jax ? reverse-engineered prompt

I want to build a Python library for high-performance numerical computing and machine learning. It should work a lot like NumPy but be supercharged to run on accelerators. The main idea is that it provides a set of function transformations for my existing Python and NumPy code.

For example, I'd want a jit function that just-in-time compiles my code to run much faster on GPUs and TPUs. It also needs a powerful automatic differentiation system. I should be able to wrap any function in something like grad to get its gradients, which is essential for training ML models. Another key feature would be vmap for automatic vectorization, so I don't have to manually manage batch dimensions. Most importantly, all these tools should be composable, so I could, for example, get a JIT-compiled, vectorized gradient function for super-efficient training.