Muller's recurrence

muller_recurrence.py

from decimal import Decimal
from fractions import Fraction


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


N = 25

x_prev = 4
x_curr = 4.25

x_prev_dec = Decimal(4)
x_curr_dec = Decimal(17)/Decimal(4)

x_prev_frac = Fraction(4)
x_curr_frac = Fraction(17, 4)

for i in range(2, N+1):
    x_next = muller_recurrence(x_curr, x_prev)
    x_prev, x_curr = x_curr, x_next

    x_next_dec = muller_recurrence(x_curr_dec, x_prev_dec)
    x_prev_dec, x_curr_dec = x_curr_dec, x_next_dec

    x_next_frac = muller_recurrence(x_curr_frac, x_prev_frac)
    x_prev_frac, x_curr_frac = x_curr_frac, x_next_frac

    print(f"{i} | {x_next} | {x_next_dec} | {float(x_next_frac)}")

(EN) The problem of rounding a row of irrational numbers: https://latkin.org/blog/2014/11/22/mullers-recurrence-roundoff-gone-wrong/
(RU) Проблема округления ряда иррациональных чисел: https://habr.com/post/258483/