I'm not sure this is worth worrying about. We already have a very tight error bound on the result: if `x` is a (positive) fraction and `y` is the closest float to x, (and assuming IEEE 754 binary64, round-ties-to-even, no overflow or underflow, etc.) then `math.sqrt(y)` will be in error by strictly less than 1 ulp from the true value √x, so we're already faithfully rounded. (And in particular, if the std. dev. is exactly representable as a float, this guarantees that we'll get that standard deviation exactly.)