To be clear: the assignment isn't the optimization; its the use of a symbol for 'x' on the rhs so that the compiler can recognize it. To illustrate that

    X &x = { complex reference expression for x }
    y = (x + 1) / atan(x) - x;

Now the compiler has the clues it needs to write good code. And with language support I don't have to introduce new names for each occurrence; just one name like <LHS> that readers can quickly learn.