Muller's Recurrence in python -- https://latkin.org/blog/2014/11/22/mullers-recurrence-roundoff-gone-wrong/

floating_roundoff.py

from fractions import Fraction

def f(y, z):
    return 108 - (815 - 1500 / z) / y

# Initialize exact values using Fraction for exact arithmetic
xExact = {0: Fraction(4), 1: Fraction(17, 4)}

# Initialize floating point values
xFloat = {0: 4.0, 1: 4.25}

for n in range(2, 101):
    xExact[n] = f(xExact[n-1], xExact[n-2])
    xFloat[n] = f(xFloat[n-1], xFloat[n-2])

table = []
for i in range(101):
    table.append([i, float(xExact[i]), round(xFloat[i], 20)])

# Print the table with headers
headers = ["i", "x[i] \"exact\"", "x[i] floating point"]
print(f"{headers[0]:<5} {headers[1]:<25} {headers[2]:<25}")
for row in table:
    print(f"{row[0]:<5} {row[1]:<25} {row[2]:<25}")

https://news.ycombinator.com/item?id=17637441