poormans-sine.py

import math
import random

FAC3 = 6.
FAC5 = 120.
FAC7 = 5040.

def poorMenSine(x):
    return x - (x ** 3 / FAC3) + (x ** 5 / FAC5) - (x ** 7 / FAC7)

nIter = 1_000_000

deltaMax = 0.
deltaMin = math.inf
deltaSum = 0.

for _ in range(nIter):
    v = random.uniform(-math.pi, math.pi)
    delta = abs(math.sin(v) - poorMenSine(v))

    deltaSum += delta

    if delta > deltaMax:
        deltaMax = delta

    if delta < deltaMin:
        deltaMin = delta

print("Avg/min/max delta: {:.2e}/{:.2e}/{:.2e}"
        .format(deltaSum/ nIter, deltaMin, deltaMax))