SICP Exercise 1.8

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

(define (improve guess x)
  (/ (+ (/ x (square guess))
        (* 2 guess))
     3))

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

(define (cube x)
  (* x x x))

(define (good-enough? guess prev-guess)
  (< (abs (- guess prev-guess)) 1e-6))

(define (cuberoot x)
  (cuberoot-iter 1.0 0.0 x))

;; test
(cuberoot 27)
(cube (cuberoot 1000))
(cuberoot 0.001)
(cuberoot 100000000000000000)

1 ]=> ;; test
(cuberoot 27)
;Value: 3.0000000000000977

1 ]=> (cube (cuberoot 1000))
;Value: 1000.0000000000005

1 ]=> (cuberoot 0.001)
;Value: .10000000000000005

1 ]=> (cuberoot 100000000000000000)
;Value: 464158.88336127787