> Ordinary testing using a few handpicked example

Ah, but if you have specifications, you should have the ability to generate unlimited numbers of tests. Handpicked examples aren't needed. The great advance in testing with increase in compute power was the realization that carefully handcrafted tests are silly; just blast huge amounts of randomness at the system and use cheap compute to save expensive human effort.

I think it's a common experience to implement some well-defined data structure or algorithm and use the clear specification of its behavior to randomly test it, to then discover this flushes out all the bugs.