Physical interpretation of geometric mean… you have a collection of multiplicative speedups, and some of them apply to any given workload. I think the geometric

Physical interpretation of geometric mean… you have a collection of multiplicative speedups, and some of them apply to any given workload. I think the geometric mean falls out of the resulting statistical distribution in a natural way but I’m sleep-deprived at the moment and can’t write out the math. Like, in this distribution geomean is the median speedup. Think of the case with two values, 2.00 and 2.42. Decompose it into three speedups… 2x, 1.1x, and 1.1x. The speedup 2x happens with probability 1. Each of the 1.1x speedups happen with probability 0.5. The geomean is 1 2x speedup and 1 1.1x speedup, giving 2.2x. There are many such decompositions, that one is not unique. Exercise for the reader to show which conditions give you the geometric mean and explain why that is reasonable… I’m terribly sleep-deprived at the moment and this is where I stop. There is of course no correct choice of mean here, just a bunch of different choices with different interpretations justifying them.