> Is the compiler smart enough to only compute them whenever it is necessary?

This is known as "code sinking," and most optimizers are capable of doing this. Except keep in mind that a) the profitability of doing so is not always clear [1] and b) the compiler is a lot more fastidious about corner-case behavior than you are, so it might conclude that it's not in fact safe to sink the operation when you think it is safe to do so.

[1] If the operation to sink is x = y + z, you now may need to keep the values of y and z around longer to compute the addition, increasing register pressure and potentially hurting performance as a result.