For quite a few cases, the "symbolic" route might be the future. In Python for example there is sympy, which is mostly a computer aided algebra toolkit, but it

For quite a few cases, the "symbolic" route might be the future. In Python for example there is sympy, which is mostly a computer aided algebra toolkit, but it can translate formulas to Fortran, Theano and Javascript. Theano on the other hand is also a symbolic toolkit designed to make linear algebra super-fast. It takes a symbolic representation of the computations, and then compiles it into C code or Cuda for GPUs. Theano has been used extensively in deep learning, but it has other applications as well. PyMC is a library implementing Bayesian inference through monte carlo methods. Version 3 implements samplers based on Theano. The advantage here is that Theano can automatically deduce derivatives, which allows for more sophisticated algorithms and better performance.