Fastest formula?

[M Benesi]

  I've tried out algebraic write outs (a long time ago) but they seemed to drop off in performance rather quickly (compared to the trig version) for higher n (but that may be due to lack of optimization on my part).

  The trig version takes twice as long as the complex triplex version for just about all z^n that I've tried (up to z^17- need to write optimizations for everything above z^16 in ChaosPro). 

  What I call the complex triplex version might be the same thing that David Makin calls the "crazy double complex" version, but I've not been able to pinpoint the exact math of the "crazy" version as of yet, so don't know (and don't want to bother David with pesky questions). 

  I do know the complex triplex version runs pleasantly fast, and it's REALLLLLY nice for the 4d version (faster than the 3d trig version), which makes extensions to higher dimensions a lot easier.. and nice.  I don't know how it would do on modern GPUs, which might do the trig versions faster, which would render the complex triplex version obsolete (well, for anyone with a computer with a modern GPU). 

  Anyways...