here my consideration (see attached image comparing the code and the passes executed for the test cases).
I did some test cases, at the moment my code seems the shorter in execution
In particular if X=Y=0 is quickly evaluated... instead of pass through all the code.
your code seems suffering from point-2 I highlighted in previous post, that is even if some value computation are ended you still go through the code
I attached also a mini project (LAZ 2.2.2/fpc 3.2.2) where some attempt in evaluation arctan routines is done (PS: note that ARCTAN2 of lazarus is executed because I working on Win10 64 bit, other OS have different implementation)
in the code you can put X and Y values as you like and in the code of right button you can select the routine you like to execute.
Obviously all the above if I am not wrong !