#lang sicp
(define tolerance 0.00001)
(define (fixed-point f guess)
  (define new-guess (f guess))
  (cond ((< (abs (- guess new-guess)) tolerance)
         (display new-guess)
         (newline)
         (f guess))
        (else
         (display new-guess)
         (newline)
         (fixed-point f new-guess))))

; 34 steps without damping
(define solution (fixed-point
                             (lambda (x) (/ (log 1000)
                                            (log x)))
                             2.0))
(newline)
(newline)
(newline)
; 9 steps with average damping
(define solution-damped
        (fixed-point (lambda (x) (/ (+ x
                                       (/ (log 1000)
                                          (log x)))
                                    2.0))
                     2.0))