; Now let’s formalize the process in terms of procedures. We start with a value for the radicand (the number whose square root we are trying to compute) and a value for the guess. If the guess is good enough for our purposes, we are done; if not, we must repeat the process with an improved guess. We write this basic strategy as a procedure:
(define (improve guess x)
(average guess (/ x guess)))
(define (average x y)
(/ (+ x y) 2))
(define (square x)
(* x x))
(define (good-enough? guess x)
(< (abs (- (square guess) x)) 0.001))
(define (sqrt-iter guess x)
(if (good-enough? guess x)
; return guess
guess
; otherwise
(sqrt-iter (improve guess x) x
)))
(define (sqrt x)
(sqrt-iter 1.0 x))
(sqrt 9)