Well, for some reason it doesnt let me respond to the child comments :(

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.

Of course you can. You can write test cases for anything.

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.