Given a set of natural numbers $S=\{n_1,n_2,\ldots,n_m\}$ and a target number $n$, the goal is to compute the target number using only elemental operations, namely $+,-,*,/,(,)$ and numbers from $S$. A second goal would be to minimize the numbers to be used from $S$. Numbers from $S$ can be taken more than once but each extra copy counts towards the number of numbers used.
Of course one way would be to brute force it but the number of computations get wild pretty fast. I was hoping to get some pointers on how to do this more efficiently or if impossible, a way to get 'good' (near the minimum) solutions.