I'm not sure if this will help anything, as it doesn't answer a darned thing you're asking about. I waited to see if someone else would respond to this, but nobody did. So, we'll see if this helps.
I'm a retired mathematician. My company modeled traffic. We used sanity checks.
Let's say you're trying to find the square root of 224. A sanity check tells you that the answer can't be 224. It can't be 1. It can't be 2340. It has to be within a certain range. Anything outside that range fails the sanity check. By simply knowing what the answer should be in approximation, let's say somewhere between 10 and 20, you can eliminate large swaths of answers as being the wrong answer simply by doing a sanity check.
In programming, if we know it's outside the bounds of sanity, we exit the program with a fault. We put sanity checks in because humans are flawed and it's a good way to reduce errors.