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- #lang racket
- (define (Mb-to-B n) (* n 1024 1024))
- (define MAX-BYTES (Mb-to-B 64))
- (custodian-limit-memory (current-custodian) MAX-BYTES)
- (define tolerance 0.0000000001)
- (define (fixed-point f guess)
- (define (close-enough? value1 value2)
- (< (abs (- value1 value2)) tolerance))
- (define (try current-guess)
- (display current-guess) (newline)
- (let
- ((next (f current-guess)))
- (if
- (close-enough? current-guess next)
- next
- (try next))))
- (try guess))
- (define (xx x)
- (/ (log 1000) (log x)))
- ;; defines a value
- (define x-power-x-is-1000
- (fixed-point xx 2.0))
- (define (average a b)
- (/ (+ a b) 2))
- (define x-power-x-is-1000-avg-damping
- (fixed-point
- (lambda (x) (average (xx x) x))
- 2.0))
- ;; prints the value
- x-power-x-is-1000
- x-power-x-is-1000-avg-damping
- ; 2.0
- ; 9.965784284662087
- ; 3.004472209841214
- ; 6.279195757507157
- ; 3.759850702401539
- ; 5.215843784925895
- ; 4.182207192401397
- ; 4.8277650983445906
- ; 4.387593384662677
- ; 4.671250085763899
- ; 4.481403616895052
- ; 4.6053657460929
- ; 4.5230849678718865
- ; 4.577114682047341
- ; 4.541382480151454
- ; 4.564903245230833
- ; 4.549372679303342
- ; 4.559606491913287
- ; 4.552853875788271
- ; 4.557305529748263
- ; 4.554369064436181
- ; 4.556305311532999
- ; 4.555028263573554
- ; 4.555870396702851
- ; 4.555315001192079
- ; 4.5556812635433275
- ; 4.555439715736846
- ; 4.555599009998291
- ; 4.555493957531389
- ; 4.555563237292884
- ; 4.555517548417651
- ; 4.555547679306398
- ; 4.555527808516254
- ; 4.555540912917957
- ; 4.555532270803653
- ; 4.555537970114198
- ; 4.555534211524127
- ; 4.555536690243655
- ; 4.555535055574168
- ; 4.5555361336081
- ; 4.555535422664798
- ; 4.5555358915186215
- ; 4.555535582318266
- ; 4.555535786230128
- ; 4.555535651754059
- ; 4.555535740438517
- ; 4.5555356819527715
- ; 4.555535720523029
- ; 4.555535695086664
- ; 4.555535711861472
- ; 4.555535700798798
- ; 4.555535708094425
- ; 4.555535703283096
- ; 4.5555357064560775
- ; 4.555535704363555
- ; 4.555535705743535
- ; 4.5555357048334635
- ; 4.5555357054336385
- ; 4.555535705037834
- ; 4.55553570529886
- ; 4.555535705126719
- ; 4.555535705240242
- ; ==> 62 steps
- ; 2.0
- ; 5.9828921423310435
- ; 4.922168721308343
- ; 4.628224318195455
- ; 4.568346513136242
- ; 4.5577305909237005
- ; 4.555909809045131
- ; 4.555599411610624
- ; 4.5555465521473675
- ; 4.555537551999825
- ; 4.555536019631145
- ; 4.555535758730802
- ; 4.555535714310077
- ; 4.555535706747033
- ; 4.555535705459354
- ; 4.555535705240114
- ; 4.555535705165376
- ; 4.555535705202788
- ; ==> 18 steps
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