(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 x) (cdr x))
(define (lower-bound x) (car x))

; 1 ]=> (add-interval (make-interval 1 3) (make-interval 0 0.5))
; 
; ;Value: (1 . 3.5)
; 
; 1 ]=> (mul-interval (make-interval -1 1) (make-interval 4 5))
; 
; ;Value: (-5 . 5)
; 
; 1 ]=> (div-interval (make-interval 3 4) (make-interval 5 6))
; 
; ;Value: (.5 . .8)