now we have to do less trigonometric calculations. what is most important, sine and cosine functions of the same real number can be evaluated in just one step using fpu instruction fsincos. using good implementation we can use this trick also with hiperbolic functions. but its not enough, because we can still do some further simplifications. which are related with arguments of used trigonometric functions. as we can see above, we have addition or subtraction of two complex numbers defined in skull fractal formula. in our case it is easy to show that these two operations can be expressed as :
there cis(a)=cos(a)+isin(a). After shown operations my XaoS port rendered skull fractal much faster.