In theory you cannot even say for all programs and all inputs if the program will finish the calculation [0]. In practice you often can break it down but the number of combinations of input is what makes it impossible to test everything. Most developers try to keep individual functions as small as possible to understand them easier. You can use math to do formal verification, but that gets difficult with real programs too.
[0] https://en.wikipedia.org/wiki/Halting_problem