Can you get pi from e

I got this one from rec.puzzles. If you want to see some great answers, the link is part of the title.

Using only the constant e (the base of natural logarithms, 2.71828...) a
dozen times, plus addition, multiplication, subtraction, division,
exponentiation, and parentheses, create an expression that comes as close as
possible to the value of pi (3.14159...). Other operations or constants are
not allowed (no roots, absolute values, imaginary numbers, etc.). The
constant e must appear exactly twelve times.

For example:

(e+e+e+e+e+e)/(e+e)+e+e-e-e = 3

Which differs from pi by less than 0.15. I'm sure than someone can do
better.

Carl G.

Tags: math, puzzle