Does gcc optimize c++ code algebraically and if so to what extent?

Question

Consider the following piece of code showing some simple arithmetic operations

    int result = 0;

    result = c * (a + b) + d * (a + b) + e;

Answer 1

Yes, optimizers, gcc's included, do optimizations of this type. Not necessarily the expression that you quoted exactly, or other arbitrarily complex expressions. But a simpler expresion, (a + a) - a is likely to be optimized to a for example. Another example of possible optimization is a*a*a*a to temp = a*a; (temp)*(temp)

Whether a given compiler optimizes the expressions that you quote, can be observed by reading the output assembly code.

No, this type of optimization is not used with floating points by default (unless maybe if the optimizer can prove that no accuracy is lost). See Are floating point operations in C associative? You can let for example gcc do this with -fassociative-math option. At your own peril.