2.13.rkt

#lang sicp

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

(define (upper-bound p)
  (cdr p))

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

(define (make-center-width c w)
  (make-interval (- c w) (+ c w)))

(define (center i)
  (/ (+ (lower-bound i) (upper-bound i)) 2))

(define (width i)
  (/ (- (lower-bound i) (upper-bound i)) 2))

(define (make-center-percent c p)
  (make-interval (- c (* c (/ p 100.0))) (+ c (* c (/ p 100.0)))))

(define (percent i)
  (* (/ (- (upper-bound i) (center i)) (center i)) 100.0))

(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 i1 (make-center-percent 100000 0.001))
(define i2 (make-center-percent 10 0.002))

(define test (mul-interval i1 i2))

(percent test) ; tolerance1 + tolerance 2