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import math

from collections.abc import Callable

def intersection(function: Callable[[float], float], x0: float, x1: float) -> float:

"""

function is the f we want to find its root

x0 and x1 are two random starting points

>>> intersection(lambda x: x ** 3 - 1, -5, 5)

0.9999999999954654

>>> intersection(lambda x: x ** 3 - 1, 5, 5)

Traceback (most recent call last):

...

ZeroDivisionError: float division by zero, could not find root

>>> intersection(lambda x: x ** 3 - 1, 100, 200)

1.0000000000003888

>>> intersection(lambda x: x ** 2 - 4 * x + 3, 0, 2)

0.9999999998088019

>>> intersection(lambda x: x ** 2 - 4 * x + 3, 2, 4)

2.9999999998088023

>>> intersection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)

3.0000000001786042

>>> intersection(math.sin, -math.pi, math.pi)

0.0

>>> intersection(math.cos, -math.pi, math.pi)

Traceback (most recent call last):

...

ZeroDivisionError: float division by zero, could not find root

"""

x_n: float = x0

x_n1: float = x1

while True:

if x_n == x_n1 or function(x_n1) == function(x_n):

raise ZeroDivisionError("float division by zero, could not find root")

x_n2: float = x_n1 - (

function(x_n1) / ((function(x_n1) - function(x_n)) / (x_n1 - x_n))

)

if abs(x_n2 - x_n1) < 10**-5:

return x_n2

x_n = x_n1

x_n1 = x_n2

def f(x: float) -> float:

return math.pow(x, 3) - (2 * x) - 5

if __name__ == "__main__":

print(intersection(f, 3, 3.5))