IIRC, I've done just the float version of it floating somewhere (in your test routine biggest error was 2.319926441174402498290874063968658447265625e-06)
Hmm... do you mean sN := Truncate(Exp(z+O(z^N)));
Note: Exp() approximation using Taylor and Remez needs to be implemented as 'order' 13 and using double precicion to get accurate approximation.