Erm, sure I know that name from somewhere! I won't dispute your claims about alternative methods, but I've found it hard to find any open documentation about this stuff, so I am unaware of it myself. Then again, I hereby announce that I am an _amateur_ at this, so I'm not taking criticism personally!

In fact one of the reasons I wrote my stuff (FWIW in c and Python) is because I couldn't follow the code in TaylorIntegration.jl ;) My stuff is _really_ simple, and I know _exactly_ how it works.