Sounds like the typical case of someone not understanding Mathematica. The 40min -> 5sec speed up can typically be achieved in Mathematica just by changing 1 to

Sounds like the typical case of someone not understanding Mathematica. The 40min -> 5sec speed up can typically be achieved in Mathematica just by changing 1 to 1. The default is slower but always completely accurate, which is important for math, but less so for most numerical scripts. If that fails Mathematica can also just compile your script for you.