sicp-2.1.4

(define (add-interval x y)
   (make-interval (+ (lower-bound x) (lower-bound y))
                  (+ (upper-bound x) (upper-bound y))))

(define (mul-interval x y)
   (let ((p1 (* (lower-bound x) (lower-bound y)))
         (p2 (* (lower-bound x) (upper-bound y)))
         (p3 (* (upper-bound x) (lower-bound y)))
         (p4 (* (upper-bound x) (upper-bound y))))
     (make-interval (min p1 p2 p3 p4)
                    (max p1 p2 p3 p4))))

(define (div-interval x y)
   (mul-interval x
                 (make-interval (/ 1.0 (upper-bound y))
                                (/ 1.0 (lower-bound y)))))

(define (make-interval a b) (cons a b))

(define upper-bound cdr)

(define lower-bound car)

(define (sub-interval x y)
   (make-interval (- (lower-bound x) (lower-bound y))
                  (- (upper-bound x) (upper-bound y))))

(define (span-zero? interval)
  (and (>= (upper-bound interval) 0)
           (<= (lower-bound interval) 0)))

(define (div-interval x y)
  (if (span-zero? y)
    (error "divides zero")
    (mul-interval x
                 (make-interval (/ 1.0 (upper-bound y))
                                (/ 1.0 (lower-bound y))))))