Numerically calculate fractional iterate of x^2-2

approx_fractional_iterate.py

def approxfi(x, n):
    #Apply x -> F(x) mapping until x is sufficiently large
    k = 0
    while (x < 1e14) and (k<100):
        x = x**2-2
        k += 1
    #Calculate approximate fractional iterate for large argument
    x = x**(2**n)
    #Apply reverse mapping x -> F[-1](x)
    for _ in range(k):
        x = (x+2)**0.5
    return x