Exercise 2.11: In passing, Ben also cryptically
comments: “By testing the signs of the endpoints of the intervals, it is
possible to break mul-interval into nine cases, only one of which
requires more than two multiplications.”  Rewrite this procedure using Ben’s
suggestion.

After debugging her program, Alyssa shows it to a potential user, who complains
that her program solves the wrong problem.  He wants a program that can deal
with numbers represented as a center value and an additive tolerance; for
example, he wants to work with intervals such as 3.5 
  ±
 0.15 rather than
[3.35, 3.65].  Alyssa returns to her desk and fixes this problem by supplying
an alternate constructor and alternate selectors:


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

Unfortunately, most of Alyssa’s users are engineers.  Real engineering
situations usually involve measurements with only a small uncertainty, measured
as the ratio of the width of the interval to the midpoint of the interval.
Engineers usually specify percentage tolerances on the parameters of devices,
as in the resistor specifications given earlier.