When the LLM knows how to simplify/solve the formula and the person using it doesn't, it could be much more efficient than directly running the brute-force/inefficient version provided by the user. A simple example would be summing all numbers from 0 to a billion; if you ask o1 to do this, it uses the O(1) analytical solution, rather than the naive brute-force O(n) approach.

Though even in this case, it is enormously more efficient to simply sum the first billion integers rather than find an analytic solution via a 405b parameter LLM...

Yes an llm could do it since it can predict the next token for pretty much anything. But what's the error margin you are ready to tolerate?