[samwho]

I'm actually not sure, to be honest. The post explicitly doesn't touch on the implementation of murmur3, and part of the reason is that while I can see what it's doing, I have no idea why it's doing it.

The initial announcement of murmur (https://tanjent.livejournal.com/756623.html) makes it seem like it's trial and error.

[aappleby]

Murmur author here, it is a lot of trial and error but in general you're trying to pack as much "nonlinearity" as possible into as few instructions as possible. Multiplication is commutative, xor is commutative, but if you mix the two together you get functions that are strongly non-linear (in the algebra sense) because the mathematical "spaces" of integers and bits aren't connected together the same way. Ensuring that the nonlinearity applies to all the bits roughly equally is hard and requires trial and error.