Comment by adgjlsfhk1

You really should check out Approxfun.jl and DifferentialEquations.jl. The julia ecosystem for this type of thing is incredibly well developed. You get autodiff, auto-sparsity detection, auto-vectorization and more for free. Also, these tools leverage the fact that Julia is fast and has a good macro system so the code you generate is just normal Julia code, which can be used with any of the other tools of the language. Also multiple dispatch means that you don't have to use anything complicated to write this. Just write your equations "normally" and this all just works.