Even an add_numbers function can have bugs, e.g. you have to ensure the inputs are numbers. Most coding agents would catch this in loosely-typed languages.

The problem (which should be obvious) is that with a/b real you cant construct an exhaustive input/output set. The test case can just prove the presence of a bug, but not its absence.

Another category of problems that you cant just test and have to prove is concurrency problems.

And so forth and so on.