Вычислите корень n-й степени из числа методом деления отрезка пополам

def main():
    num = float(input())
    rootDegree = int(input())
 
    eps = 0.00001
    root = num / rootDegree
    rn = num
    countiter = 0
 
    while abs(root - rn) >= eps:
        rn = num
        for i in range(1, rootDegree):
            rn = rn / root
        root = 0.5 * (rn + root)
        countiter += 1
 
    print(root)
 
if __name__ == "__main__":
    main()

def nth_root(a, n, precision=0.0001):
    left = 0
    right = max(1, a)
    mid = (left + right) / 2.0
    while abs(mid ** n - a) > precision:
        if mid ** n < a:
            left = mid
        else:
            right = mid
        mid = (left + right) / 2.0
    return mid
 
a = float(input())
n = int(input())
 
print(nth_root(a, n))

def root(a, n):
    def f(x):
        return x**n - a
 
    if a < 1:
        left = a
        right = 1
    else:
        left = 0
        right = a
    
    max_iterations = 100000
    current_iteration = 0
    while current_iteration < max_iterations:
        mid = (left + right) / 2
        if f(left) * f(mid) <= 0:
            right = mid
        else:
            left = mid
        if abs(right - left) < 0.000001:
            return round((left + right) / 2, 6)
        current_iteration += 1
    
    return "No root found in " + str(max_iterations) + " iterations."
 
a = float(input())
n = int(input())
print(root(a, n))