There is no mathematically rigorous way of proving that any given piece of code does or doesn't do anything.
Sure there is.
Sure there is.
And draw any meaningful conclusions from that data.
Better yet, how do I write reliable software that runs on a buggy processor? What do I use to test that the chip I'm making does what it is supposed to every time for all scenarios? It's programmable, after all.
That, I'm sure, you can identify with.