One can construct convincing proofs quite readily of the ultimate futility of exhaustive testing of a program and even of testing by sampling. So how can one proceed? The role of testing, in theory, is to establish the base propositions of an inductive proof. You should convince yourself, or other people, as firmly as possible, that if the program works a certain number of times on specified data, then it will always work on any data. This can be done by an inductive approach to the proof.