In some instances (e.g. integrating over a heated dark matter profile) it may be efficient to tabulate the relation between $r_\mathrm{f}$ and $r_\mathrm{i}$. To do this efficiently we would need some heuristic to decide when it is worth while to do such a tabulated approach. A simple version could be just how many times this relation has been evaluated - if more than $N$ then switch to tabulation.