# What would be the upper bounds on the accuracy of the algorithm in the below link based on the precision used in the arithmetic operations. [duplicate]

• I'd say that L4 is executed at most (number of mantissa bits) times, hence the erros accumulated in summing up $y$ are up to that times $\epsilon$, so e.g. with IEEE doubles, the relative error is $<52\cdot 2^{-52}\approx 1.2\cdot 10^{-14}$ – Hagen von Eitzen Jun 21 at 12:22