How can I improve performance via a high-level approach when implementing long equations in C++

Question

I am developing some engineering simulations. This involves implementing some long equations such as this equation to calculate stress in a rubber like material:

Answer 1

Woah, what a hell of an expression. Creating the expression with Maple actually was a suboptimal choice here. The result is simply unreadable.

1. chose speaking variable names (not l1, l2, l3, but e.g. height, width, depth, if that is what they mean). Then it is easier for you to understand your own code.
2. calculate subterms, that you use multiple times, upfront and store the results in variables with speaking names.
3. You mention, that the expression is evaluated very many times. I guess, only few parameters vary in the inner most loop. Calculate all invariant subterms before that loop. Repeat for the second inner loop and so on until all invariants are outside the loop.

Theoretically the compiler should be able to do all of that for you, but sometimes it can't - e.g. when the loop nesting spreads over multiple functions in different compilation units. Anyway, that will give you much better readable, understandable, and maintainable code.