Following my answer to this question I wondered how WolframAlpha would tell me, so promptly and with so many decimal places, the result of
I thought that maybe WolframAlpha would take the log of that, and compute instead
and then exponentiate it. But how would it still compute the logarithm of that number, and how would it then multiply with such a big number, and then raise $e$ to that power? I think I may have read somewhere (not exactly sure if my mind is tricking me) that computers use things like Taylor series for those calculations. But even if they do, those series are infinite sums! How do they do it?
Basically, my question comes down to:
What are the most common tricks/shortcuts/manipulations/approximations/... that computers do in order to provide precise answers in near-immediate time? I am thinking about things like big factorials, trigonometric functions, exponentiation, logarithms, ... Is there any good (and light), recommendable literature on this topic?
(P.S. I was not so sure of how to tag this question; if you have a suggestion, drop it in the comment section)