Investigate elementary functions

[eggrobin]

This is a very low-priority task, but it's fun.
Write approximants for elementary functions at the precisions required where they are used (the precision shall be documented).
An example of a case where a fairly imprecise approximation could be useful is found here. In addition to an _n_th root (for known n) being simpler than the general pow, last-bit precision is preposterous since safety_factor is a fudge factor (common values in the literature are 0.9, 0.75, and 0.5).
A potentially more useful operation is the inverse square root appearing in the gravitational force computation. It is however harder to estimate the precision requirement there, and the potential for improvement is likely smaller than in the case of pow.