Vector sum numerical accuracy

[msaroufim]

If we draw inputs from a normal distribution with 0 and variance 1 then the expected output is 0 with a variance of sqrt(N) where N is the number of input elements

There's a few common tricks to avoid this which we incorporated and I figured would be interesting enough to keep track of

1. Shift the distribution with a random offset
2. Instead of sampling floats we could sample integers and the values will vary much more greatly
3. Can use a mixture of distributions
4. Low tolerance as we get closer to law of large numbers

But TL;DR the knobs within our control are test distributions and mixtures of them, offset, scale, random seeds, shapes