I'm using statsmodels library for generic likelihood models. As I have a quite complicated likelihood function, I used sympy to calculate gradient and hessian for me. This works fine, but it is too slow for my needs, because likelihood function contains term b0*x0 + b1*x1 + ... + bn*xn. That way hessian size increases by N^2 and so does the complexity.
Elements of the hessian are often pretty similar like expensive_operation * x0 and expensive_operation * x1, etc. It means that if I could pre-calculate expensive_operation and use it in functions in hessian, I would drastically increase performance.
So the question is - is there a tool which would take list of functions, optimize them and then evaluate them effectively? Something like numexpr which would take list of functions?
SymPy has cse, which stands for common subexpression elimination. See the docs.
A simple example:
>>> print(cse(sin(x**2)*cos(x**2) + 2*sin(x**2) - cos(x**2)))
([(x0, x**2), (x1, sin(x0)), (x2, cos(x0))], [x1*x2 + 2*x1 - x2])