"""
Exercise 3.23 from "A primer on..." Wrap the egg formula
from earlier in a function, with M, To and Ty
as arguments and the rest of the parameters defined
as local variables inside the function. 
"""

import numpy as np

def egg(M, To=20, Ty=70):
    rho = 1.038
    c = 3.7
    K = 5.4e-3
    Tw = 100

    a = (M ** (2 / 3) * c * rho ** (1 / 3)) / (K * np.pi**2 * (4 * np.pi / 3) ** (2 / 3))
    b = np.log(0.76 * (To - Tw) / (Ty - Tw))
    t = a * b
    return t


#Loop through all the options listed in the exercise:
for Ty in 63, 70:
    for M in 47, 67:
        for To in 4, 25:
            t = egg(M=M, To=To, Ty=Ty)
            minutes = int(t / 60)
            seconds = int(t % 60)
            print(f"An egg with mass {M} and start temp {To} reaches {Ty} degrees after {minutes} minutes and {seconds} seconds")

"""
Terminal> python egg_func.py
An egg with mass 47 and start temp 4 reaches 63 degrees after 3 minutes and 59 seconds
An egg with mass 47 and start temp 25 reaches 63 degrees after 2 minutes and 32 seconds
An egg with mass 67 and start temp 4 reaches 63 degrees after 5 minutes and 2 seconds
An egg with mass 67 and start temp 25 reaches 63 degrees after 3 minutes and 12 seconds
An egg with mass 47 and start temp 4 reaches 70 degrees after 5 minutes and 13 seconds
An egg with mass 47 and start temp 25 reaches 70 degrees after 3 minutes and 46 seconds
An egg with mass 67 and start temp 4 reaches 70 degrees after 6 minutes and 36 seconds
An egg with mass 67 and start temp 25 reaches 70 degrees after 4 minutes and 46 seconds
"""