import math

def f(x):  
    return x**2+math.exp(x)+math.log(x)+math.sin(x)
def fp(x): 
    return 2.*x+math.exp(x)+1./x+math.cos(x)

x, h = 0.5, 1E-2
fp_exact = fp(x)

while h>1E-15:
    fp_numeric = (f(x+h/2.) - f(x-h/2.))/h
    print('h = %e' % h)
    print('Exact = %.16f,' % fp_exact, end=' ')
    print('Numeric = %.16f,' % fp_numeric, end=' ')
    print('diff = %.16f' % abs(fp_numeric-fp_exact))
    h /= 10.