Functions like e^x, sqrt, sin etc. are calculated via their series expansions in calculators.

These are often optimized versions of the simple theorems that were first proven, but it really does seem like there is no ultimate shortcut to finding the answer to these functions other than using lookup tables.

What would Stephen Wolfram say about the computation reducibility of these functions?

Do, for example, exponential functions require step-by-step exponential growth simulations to get the answer no matter what?