(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)))
      (display guess)
      (display  " -> ")
      (display  next)
      (newline)
      (if (close-enough? next guess)
          next
          (try next))))
  (try first-guess))

(display "Searching for fixed point of x -> log(1000)/log(x) ...")
(newline)

(define (f x) (/ (log 1000) (log x)))

(fixed-point f 2.0)

(display "Searching for fixed point using average dampening ...")
(newline)

(fixed-point (lambda (x) (/ (+ (f x) x) 2.0)) 2.0)

; Searching for fixed point of x -> log(1000)/log(x) ...
; 2. -> 9.965784284662087
; 9.965784284662087 -> 3.004472209841214
; 3.004472209841214 -> 6.279195757507157
; 6.279195757507157 -> 3.759850702401539
; 3.759850702401539 -> 5.215843784925895
; 5.215843784925895 -> 4.182207192401397
; 4.182207192401397 -> 4.8277650983445906
; 4.8277650983445906 -> 4.387593384662677
; 4.387593384662677 -> 4.671250085763899
; 4.671250085763899 -> 4.481403616895052
; 4.481403616895052 -> 4.6053657460929
; 4.6053657460929 -> 4.5230849678718865
; 4.5230849678718865 -> 4.577114682047341
; 4.577114682047341 -> 4.541382480151454
; 4.541382480151454 -> 4.564903245230833
; 4.564903245230833 -> 4.549372679303342
; 4.549372679303342 -> 4.559606491913287
; 4.559606491913287 -> 4.552853875788271
; 4.552853875788271 -> 4.557305529748263
; 4.557305529748263 -> 4.554369064436181
; 4.554369064436181 -> 4.556305311532999
; 4.556305311532999 -> 4.555028263573554
; 4.555028263573554 -> 4.555870396702851
; 4.555870396702851 -> 4.555315001192079
; 4.555315001192079 -> 4.5556812635433275
; 4.5556812635433275 -> 4.555439715736846
; 4.555439715736846 -> 4.555599009998291
; 4.555599009998291 -> 4.555493957531389
; 4.555493957531389 -> 4.555563237292884
; 4.555563237292884 -> 4.555517548417651
; 4.555517548417651 -> 4.555547679306398
; 4.555547679306398 -> 4.555527808516254
; 4.555527808516254 -> 4.555540912917957
; 4.555540912917957 -> 4.555532270803653
; Searching for fixed point using average dampening ...
; 2. -> 5.9828921423310435
; 5.9828921423310435 -> 4.922168721308343
; 4.922168721308343 -> 4.628224318195455
; 4.628224318195455 -> 4.568346513136242
; 4.568346513136242 -> 4.5577305909237005
; 4.5577305909237005 -> 4.555909809045131
; 4.555909809045131 -> 4.555599411610624
; 4.555599411610624 -> 4.5555465521473675
; 4.5555465521473675 -> 4.555537551999825