1.3.4-proced-return.rkt

#lang sicp
(define (average-damp f)
  (lambda (x)
    (average x (f x))))

(define (deriv g)
  (lambda (x)
    (/ (- (g (+ x dx)) (g x))
       dx)))

(define dx 0.00001)

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

((deriv cube) 5)

(define (newton-transform g)
  (lambda (x)
    (- x (/ (g x)
            ((deriv g) x)))))

(define (newtons-method g guess)
  (fixed-point (newton-transform g)
               guess))

;; find fixed point
(define tolerance 0.00001)

(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
    (< (abs (- v1 v2))
       tolerance))
  (define (try guess)
    (let ((next (f guess)))
      (if (close-enough? guess next)
          next
          (try next))))
  (try first-guess))

(define (fixed-point-of-transform
         g transform guess)
  (fixed-point (transform g) guess))

(define (sqrt x)
  (fixed-point-of-transform
   (lambda (y) (/ x y))
   average-damp
   1.0))

(define (sqrt-newton x)
  (fixed-point-of-transform
   (lambda (y) (- (square y) x))
   newton-transform
   1.0))