This question is intimately connected with previous one: "How to create internally optimized expression for computing with high WorkingPrecision?"
A good answer will hopefully discuss the
Experimental`NumericalFunction, which is a structure produced by
FindMinimumfrom the function and its
Jacobianthat is optimized for fast numerical evaluation. I know almost nothing about these objects or how to create/use them, but I would like to find out.
From other questions on this site it is apparent that other built-in numerical functions also use
Experimental`NumericalFunction which seems to be a standard way to optimize numerical evaluation. It is not documented but it is placed in the
Experimental context which "contains functions that are being considered for official inclusion in future versions of Mathematica". This undocumented function is of crucial importance because currently it is the only way to optimize arbitrary precision calculations. For
MachinePrecision we have
Compile but nothing documented for arbitrary precision. How to work with