SICP习题 1.7 (求平方根改进)

(define (sqrt-iter guess x)
(if (good-enough? guess (improve guess x))
(improve guess x)
(sqrt-iter (improve guess x)
x)))

(define (improve guess x)
(average guess (/ x guess)))

(define (average x y)
(/ (+ x y) 2))

(define (good-enough? old-guess new-guess)
(> 0.01
(/ (abs (- new-guess old-guess))
old-guess)))

(define (sqrta x)
(sqrt-iter 1.0 x))

(define (square x)
(* x x))

(sqrta 0.00009)

 

不再检测猜测值 guess 的平方与 x 之间的差，而是检测新旧两次猜测值之间的比率，当比率变化非常小时，程序就停止 improve