newton.scm

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

(define (abs x)
  (cond ((< x 0) (- x))
        ((>= x 0) x)))

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

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

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

(define (powpow x pow acc)
  (cond ((= pow 0) acc)
        ((> pow 0) (powpow x (- pow 1) (* x acc)))))

(define (power x y)
  (powpow x y 1))

(define (good-enough? guess x)
  (< (abs (- (square guess) x)) (power (/ 1 10) 10)))

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

(print (sqrt 9))
(print (sqrt 2))