import math

def deriv2(f,x,h):
  return (f(x+h)-f(x-h))/2/h

def deriv(f,x):
  h=max(math.fabs(x),math.fabs(f(x)))/2**15
  if h==0: h=1e-30
  h=((x+h)-(x-h))/2
  d1=deriv2(f,x,h)
  h=h/2
  h=((x+h)-(x-h))/2
  d2=deriv2(f,x,h)
  return (4*d2-d1)/3

x=.7

print deriv(math.cos,x), deriv(math.cos,x)+math.sin(x)