Why not one step further, and let the original formula be the code? Directly compilable Latex:

    \vec r = \frac {n_{1}}{n_{2}} \cdot (\vec v - dot(\vec v, \vec n) \cdot \vec N) - \sqrt{1 - \frac {n_{1}^2}{n_{2}^2} \cdot (1 - dot(\vec v, \vec n))} \cdot \vec N

(This is partly a joke and partly a serious suggestion, there are definitely people out there who would find that easier to write, especially if the IDE rendered it properly. I stole it by searching for ni_over_nt and finding http://viclw17.github.io/2018/08/05/raytracing-dielectric-ma... )