Suppose I am given a large integer $n$ and a small positive value $\epsilon$ such that I am to compute $\frac{1}{n}$, and then compute the reciprocal of that, in order to recover $n$ to within an accuracy of $\epsilon$.
My question is: What precision would be required in the initial computation of $\frac{1}{n}$, and then in the subsequent calculation of its reciprocal, in order recover $n$ to within \epsilon?