import numpy as np
import matplotlib.pyplot as pt

def f(x):
    return np.exp(x) - 2

def df(x):
    return np.exp(x)

xgrid = np.linspace(-2, 3, 1000)
pt.grid()
pt.plot(xgrid, f(xgrid))

xtrue = np.log(2)
print(xtrue)
print(f(xtrue))

errors = []
x = 2

x = x - f(x)/df(x)
print(x)
errors.append(abs(x-xtrue))
print(errors[-1])

for err in errors:
    print(err)

# Doubles number of digits each iteration: probably quadratic.

for i in range(len(errors)-1):
    print(errors[i+1]/errors[i]**2)