gistfile1.scm

(define (rationalize1 x e)
  (define (refine lo hi)
    (let* ([M (/ (+ (numerator lo) (numerator hi))
                 (+ (denominator lo) (denominator hi)))]
           [delta (abs (- x M))])
      (cond
       [(<= delta e) M] ;; found
       [(< M x) (refine M hi)]
       [else    (refine lo M)])))
  (if (< (abs (- x (round x))) e)
    (round->exact x)
    (refine (floor->exact x) (ceiling->exact x))))