Joerg Arndt wrote:
binsplit wins routinely whenever applicable, mostly for its memory locality. There are, however, things where (to my knowledge) no binsplit based algorithm can be used. So it is fine to also know about the performance of the AGM.
To me it looks like the AGM is based on mathematical properties of particular algebraic curves. Whereas binsplit is a general technique that provides fast evaluation of any holonomic function (with algebraic initial conditions at an algebraic point) at regular and even at singular points. These are resuls from Joris van der Hoeven [1] (see the three papers Fast evaluation of holonomic functions Fast evaluation of holonomic functions near and in singularities Efficient accelero-summation of holonomic functions there). Bruno [1] http://www.math.u-psud.fr/~vdhoeven/