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Fri Mar 8 13:24:40 EST 2013

## Exponentials: approximation error should not introduce instability

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.

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