import math
import numpy as np

def main():
    eps = np.finfo(np.float64).eps
    u = eps / 2
    print(f"u = {u:.37e}")
    
    x = (1 + u) + u
    y = 1 + (u + u)
    print(f"x = (1+u)+u = {x:.52e}")
    print(f"y = 1+(u+u) = {y:.52e}")
    print(f"y-x = {y - x:.36e}")

    a = 2.0
    b = 3.0
    x = math.sqrt(math.sqrt(a) + math.sqrt(b) - math.sqrt(a + b + 2 * math.sqrt(a * b)))
    print(f"a = {a:.5e} b = {b:.5e}")
    print(f"sqrt(sqrt(a)+sqrt(b)-sqrt(a+b+2*sqrt(a*b))) = {x:.12e}")

if __name__ == "__main__":
    main()