Non-deterministic conic fitting. runs something like 320,000,000 iterations to determine a conic section which fits a set of data points.

amb-conic.scm

;; The following definition for amb, assert and other operators are from Teach Yourself Scheme in Fixnum Days by Dorai Sitaram.

(define amb-fail '())

(define initialize-amb-fail
  (lambda ()
    (set! amb-fail
      (lambda ()
        (error "amb tree exhausted")))))

(initialize-amb-fail)

(define-macro amb
  (lambda alts
    `(let ((+prev-amb-fail amb-fail))
       (call/cc
        (lambda (+sk)
          ,@(map (lambda (alt)
                   `(call/cc
                     (lambda (+fk)
                       (set! amb-fail
                         (lambda ()
                           (set! amb-fail +prev-amb-fail)
                           (+fk 'fail)))
                       (+sk ,alt))))
                 alts)
          (+prev-amb-fail))))))

(define assert
  (lambda (pred)
    (if (not pred) (amb))))

(let ((a (amb -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 
                1 2 3 4 5 6 7 8 9 10))
      (b (amb -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 
                1 2 3 4 5 6 7 8 9 10))
      (c (amb -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 
                1 2 3 4 5 6 7 8 9 10))
      (d (amb -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 
                1 2 3 4 5 6 7 8 9 10))
      (e (amb -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 
                1 2 3 4 5 6 7 8 9 10))
      (f (amb -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 
                1 2 3 4 5 6 7 8 9 10))
      (conic (lambda (x y a b c d e f) 
        (+ 
            (* a (expt x 2))
            (* b x y)
            (* c (expt y 2))
            (* d x)
            (* e y)
            f))))
    (assert (= 0 (conic -2 4 a b c d e f)))
    (assert (= 0 (conic -1 1 a b c d e f)))
    (assert (= 0 (conic 0 0 a b c d e f)))
    (assert (= 0 (conic 1 1 a b c d e f)))
    (assert (= 0 (conic 2 4 a b c d e f)))
    (list a b c d e f)) ;; ax^2 + bxy + cy^2 + dx + ey + f = 0

I used code for the amb operator and such from Teach Yourself Scheme in Fixnum Days by Dorai Sitaram.