approximation exp'(x) ~= exp(x) s.t. |exp'(x)| < |exp(x)| One question that bugs me is that exp(x) = exp(x/2) * exp(x/2). The smaller the argument of x gets, the faster the series converges. At what point does this successive squaring get imprecise? I.e. exp(x/2^n) might be more precise, but the squaring looses information again.