i am not well versed in the math involved, but IMO if the outcome depends mostly on the differences between them numbers, as smaller-or-bigger distinction as well as their magnitudes, then exactness might not be needed. i mean, as long as the approximate "function" looks similar to the exact one, that might be good enough.
Maybe even generate a table of the approximate results and use that, in various stages? Like the way sin/cos was done 30y ago before FP coprocessors arrived