Fully polynomial randomized approximation scheme ($\mathbb{P}((1-\epsilon )Z\le \hat{Z}\le (1+\epsilon )Z)\ge 1-\delta$)

For a nonnegative counting quantity $Z$, an FPRAS is a randomized algorithm with the displayed guarantee, running in time polynomial in encoded input length, ${\epsilon }^{-1}$ and $\log ({\delta }^{-1})$. The usual constant-success definition is equivalent by independent repetition and a median. This counting notion differs from a deterministic fully polynomial-time approximation scheme for optimization.