(define (iterative-improve good-enough? improve)
  (lambda (first-guess)
    (define (try guess)
      (let ((improved-guess (improve guess)))
	(if (good-enough? guess improved-guess)
	    guess
	    (try improved-guess))))
    (try first-guess)))

(define (sqrt-ave x)
  (define (good-enough? x y)
    (let ((tolerance 0.00001))
      (< (abs (- x y)) tolerance)))
  (define (improve guess)
    (average guess (/ x guess)))
  ((iterative-improve good-enough? improve) 1.0))

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


(define (fixed-point f first-guess)
  (define (close-enough? v1 v2)
    (< (abs (- v1 v2)) tolerance))
  ((iterative-improve close-enough? f)
    first-guess))

(define (average-damp f)
  (lambda (x) (average x (f x))))

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