import numpy as np
import matplotlib.pyplot as pt

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

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
xbefore = 3

slope = (f(x)-f(xbefore))/(x-xbefore)

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

for err in errors:
    print(err)

# Does not quite double the number of digits each round--unclear.

for i in range(len(errors)-1):
    print(errors[i+1]/errors[i]**1.618)