Rules for dervative of asec and acsc with complex input incorrect?

[oxinabox]

Found when doing #76

asec

x = 1.6 - 0.8im
(central_fdm(5, 1))(asec, x) = 0.16078185380606091 + 0.29837305540037473im
(last(frule(asec, x)))(1) = 0.27724414876919296 + 0.19496914288010564im

WolframAlpha says 0.160782 + 0.298373 i
Argreeing with the central_fdm

acsc

x = 1.6 - 0.8im
(central_fdm(5, 1))(acsc, x) = -0.16078185380578297 - 0.29837305540024617im
(last(frule(acsc, x)))(1) = -0.27724414876919296 - 0.19496914288010564im

WolframAlpha says -0.160782 - 0.298373 i
Argreeing with the central_fdm

@simeonschaub do you know what is going on here?
It has been years since I did complex calculus

[oxinabox]

Investigating further.
This is basically because we use a simplification of the derviative that only works for real numbers.
So it is just wrong in the general case.

[oxinabox]

I have a fix, and will include it in my PR fro #76