Square-rooting in Racket

mysqrt.rkt

#lang racket

(define (mysqrt x)
  ;; a procedure to calculate square root of a number
  ;; starts with a guess and improves it until it is good enough
  
  ;; a guess can be improved by averaging itself with x/guess
  (define (avg a b) (/ (+ a b) 2.0))
  (define (improve-guess guess x) (avg guess (/ x guess)))

  ;; a guess is good enough when guess^2 tends to x
  (define (good-enough? guess x) (< (abs (- (* guess guess) x)) 0.0001))

  ;; try and improve the guess until it is good enough 
  (define (try-guess guess x)
    (if (good-enough? guess x) guess
      (try-guess (improve-guess guess x) x)))

  ;; start with guess = 1
  (try-guess 1.0 x))

Hmm.

#!/usr/bin/env python3

def avg(a, b):
    return (a + b) / 2.0

def improve_guess(guess, x):
    return avg(guess, x / guess)

def is_good_enough(guess, x):
    return abs(x - (guess * guess)) < 0.0001

def try_guess(guess, x):
    return guess if is_good_enough(guess, x) else try_guess(improve_guess(guess, x), x)

>>> try_guess(1.0, 26)
5.099019513684702