#!/usr/bin/env python3

import numpy as np
import matplotlib.pyplot as plt


# Truncation of Euler's Constant
e_OEIS = 2.7182818284590452353
N_max = 25
N_range = np.arange(0, N_max)

# a) Simple Relative Error Determine
e_approx = np.zeros(N_max)
rel_err = np.zeros(N_max)

prev_e = 0
for i, n in enumerate(N_range):
    e_approx[i] = prev_e + 1/np.math.factorial(n)

    rel_err[i] = abs( e_approx[i] - e_OEIS ) / e_OEIS
    prev_e = e_approx[i]

print(e_approx)

fig, ax = plt.subplots()
ax.plot(N_range, rel_err)
ax.set_yscale('log')
ax.grid()
ax.set_ylabel("Relative Error")
ax.set_xlabel("N")

plt.show()


# b) Varying Floating Point Precision