why doesn't it shows no result,but shows no error

Question

I have written a code to get a root of a function.But it doesn't show any result.neither does it shows any error:

import math
from math import e
#finding root of f(x)=(e**-x)-x:
#f'(x)=(-e**-x)-1
#y=x-(f(x)/f'(x))
def f(x):
    x=0
    y=x-(((e**-x)-x)/((-e**-x)-1))
    z=((y-x)/y)*100
    while z<(10**-8):
        print(f"The root is {y}")
        x=y
    

Answer 1

from math import e


def f():
    x = 0
    y = x-(((e**-x)-x)/((-e**-x)-1))
    z = ((y-x)/y)*100
    print(z)
    while z < (10**-8):
        print("The root is {}".format(y))
        x = y

f()

The Output for Z is 100

Which Greater Than (10**-8) so while loop never works