First, this is taken outside of context. Second, you're trying to disprove wrong thesis.

Let's take this again into context first.

In the proper context our wrong formulae will be brought up by running functional tests by field expert (or even earlier, by programmer itself). Functional tests, as opposed to unit tests, checks validity of the program as a whole in relation to problem it should solve. So they are much fewer and quite often all external.

So this is actually no-problem.

Let me reconstruct that implicit thesis you're trying to disprove.

As I can suggest from my experience and your nickname, you're trying to disprove thesis that "types solve all problems".

But real people use types not to solve all their programming-related problems, but to solve as many of them as they see fit for the task at hand.

All software processes revolve around simple thesis: the cost of defect elimination is proportional to the time between defect introduction and defect discovery. PSP/TSP, ALL Agile processes, etc.

Type systems greatly reduce that time. As do REPL and unit-tests. But, compared to unit tests, they require much less effort from programmer.

So, yes, we all need testing. Type systems, though, reduce areal of tests to where they naturally belong.

PS In my opinion, programmer should seek strongly typed language with REPL.