2.10.rkt

#lang sicp

(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)
  (if (= (upper-bound y) (lower-bound y))
      (error "cannot divide by empty interval")
      (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 p)
  (cdr p))

(define (lower-bound p)
  (car p))

(div-interval (make-interval 1 2) (make-interval 3 3))