gistfile1.scm

(define (rationalize2 x e)

  (define (next an Qn-1 Qn-2)
    (/ (+ (* an (numerator Qn-1)) (numerator Qn-2))
       (+ (* an (denominator Qn-1)) (denominator Qn-2))))

  (if (< x 0)
    (- (rationalize2 (- x) e))
    (match (continued-fraction (exact x))
      [(a0) a0] ;integer
      [(a0 a1 . an)
       (if (<= (- x a0) e) ;integer is close enough
         a0
         (let rec ([Qn (+ a0 (/ a1))]
                   [Qn-1 a0]
                   [an an])
           (if (<= (abs (- Qn x)) e)
             Qn
             (rec (next (car an) Qn Qn-1) Qn (cdr an)))))])))