n = 1

an_prev = 1.0 # a_0

en_prev = 0.0 # e_0

while n <= N:

en = en_prev + an_prev

an = x/n*an_prev

en_prev = en

an_prev = an

n += 1

from scitools.std import factorial

e = 0

for n in range(N):

e += x**n/factorial(n)

import sys, math

x = float(sys.argv[1])

print 'exp(%g)=%g:' % (x, math.exp(x))

for N in 2, 4, 8, 16, 32, 64, 128:

print 'N=%3d exp_diffeq=%10.4e exp_sum=%10.4e' % \