[x] Some initial tests indicate that this does not converge.
[x] Check for type stability when using BigFloat to compute finite differences in tests, and profile the code when using BigFloat - right now it's rather slow.
[x] In the tests test_ttv_cartesian.jl and test_ttv_elements.jl, we should test the derivative precision versus the TTV amplitude (although not sure yet what the best metric is for this). Right now the test_ttv_cartesian fails, and this would be worse for a larger stepsize, larger number of planets, and/or longer integration time. Perhaps there is some loss of precision in the way in which the derivatives are being computed.
[x] Test of findtransit2 is failing right now. Problem seems to be occurring when the transit time occurs just after a step, so sub-step is small. Perhaps this is an issue with dh17 with small time steps? It appears to occur when some derivatives are very small, near machine precision. So perhaps not to worry about.
[x] Implement asinh comparisons.
[x] Compute transit timing derivative with time derivative of dh17 step.