From Out of the Tar Pit:
The key problem with testing is that a test (of any kind) that uses one particular set of inputs tells you nothing at all about the behaviour of the system or component when it is given a different set of inputs. The huge number of different possible inputs usually rules out the possibility of testing them all, hence the unavoidable concern with testing will always be — have you performed the right tests?. The only certain answer you will ever get to this question is an answer in the negative — when the system breaks.
This is a strong argument for some form of generative, simulation, or property-based testing.