[orbital-decay]

This is an issue with any math-related tool in general, including the specialized software, where bugs are much much more sophisticated. Most App Store/Microsoft Store/Google Play apps can't be trusted even for simple square root and trigonometry calculations.

[copperx]

I know it's totally overkill, but I use Mathematica for even simple arithmetic computations. I assume that the developers have ironed most of the obvious bugs.

[pkaye]

I think Mathematica uses the GNU multiple precision arithmetic (gmp) library itself in many cases.