celsius.py

#!/bin/env python3

import matplotlib.pyplot as plt
import seaborn as sns

def approximate_memorized(fahrenheit) -> float:
    # Nearest memorized temperature
    close = round((fahrenheit - 5) / 9) * 9 + 5
    # Convert to Celsius
    rough = (close - 32) // 9
    # Half of the difference
    diff = (fahrenheit - close) / 2
    return rough + diff

def approximate_simple(fahrenheit: float) -> float:
    return fahrenheit / 2

def exact(fahrenheit: float) -> float:
    return (fahrenheit - 32) * (5 / 9)

def main():
    fahrenheit_values = range(0, 5000)

    memorized_values = list(map(approximate_memorized, fahrenheit_values))
    simple_values = list(map(approximate_simple, fahrenheit_values))
    exact_values = list(map(exact, fahrenheit_values))

    sns.set_theme('notebook')

    # Plot the approximations
    plt.figure(1)
    sns.lineplot(x=fahrenheit_values, y=memorized_values, label='Memorized Approximation')
    sns.lineplot(x=fahrenheit_values, y=simple_values, label='Simple Approximation')
    sns.lineplot(x=fahrenheit_values, y=exact_values, label='Exact Conversion')

    plt.xlabel('Fahrenheit')
    plt.ylabel('Celsius')
    plt.title('Temperature Conversion Approximations')
    plt.legend()

    plt.show()

    # Calculate errors
    memorized_errors = [abs(m - e) / abs(e) if e != 0 else 0 for m, e in zip(memorized_values, exact_values)]
    simple_errors = [abs(s - e) / abs(e) if e != 0 else 0 for s, e in zip(simple_values, exact_values)]

    # Plot the errors as a percentage
    plt.figure(2)
    sns.lineplot(x=fahrenheit_values, y=memorized_errors, label='Memorized Approximation Error (%)')
    sns.lineplot(x=fahrenheit_values, y=simple_errors, label='Simple Approximation Error (%)')
    plt.ylim(bottom=0, top=2)
    plt.xlabel('Fahrenheit')
    plt.ylabel('Error (%)')
    plt.title('Error in Temperature Conversion Approximations')
    plt.legend()

    plt.show()

    f = 0
    while f < 100:
        memorized_error = abs(approximate_memorized(f) - exact(f))
        simple_error = abs(approximate_simple(f) - exact(f))
        if simple_error < memorized_error:
            print(f"{f:.5f}F | Simple Error = {simple_error:.4f}, Memorized Error = {memorized_error:.4f}")
            break
        f += 0.0001

if __name__ == '__main__':
    main()