The tests from Bozza et. al. 2018 are quite wasteful in the sense that there are tons of false positives. Here's an example:

The red region is where the error is > $10^{-4}$ and the grey region is where the tests says that the full calculation is necessary. I feel like there has to be a way to improve the accuracy of these tests.
Perhaps we should treat this as a machine learning prediction problem and construct physically meaningful features such as
the magnitude of the higher order terms in the multipole expansion and the value of Jacobian.
Related to #19.