I think you can model the process as a random walk, and I'd expect 2 roundings/iteration to stray away from the true value about sqrt(2) more. But it seems that

I think you can model the process as a random walk, and I'd expect 2 roundings/iteration to stray away from the true value about sqrt(2) more. But it seems that the fused iteration is actually worse than the manual one. Could be this is because of the reverse operation and inter-iteration dependencies.