gistfile1.scm

(define (rationalize3 x e)

  (define (refine xn yn an) ; returns reverse continued fraction
    (cond [(or (null? xn) (null? yn)) an]
          [(= (car xn) (car yn))
           (refine (cdr xn) (cdr yn) (cons (car xn) an))]
          [else (cons (+ 1 (min (car xn) (car yn))) an)]))

  (define (realize rcf) ; reverse continued fraction -> rational
    (fold (^[a r] (+ a (/ r))) (car rcf) (cdr rcf)))

  (if (< x 0)
    (- (rationalize3 (- x) e))
    (realize (refine (continued-fraction (exact (- x e)))
                     (continued-fraction (exact (+ x e)))
                     '()))))