ex_2_13.clj

(ns sicp.chapter-2.part-1.ex-2-13
  (:require
    [sicp.misc :as m]))

; Exercise 2.13
; Show that under the assumption of small percentage tolerances there is a simple formula for
; the approximate percentage tolerance of the product of two intervals in terms
; of the tolerances of the factors.
; You may simplify the problem by assuming that all numbers are positive.

; After considerable work, Alyssa P. Hacker delivers her finished system.
; Several years later, after she has forgotten all about it, she gets a frenzied call
; from an irate user, Lem E. Tweakit. It seems that Lem has noticed that the formula for
; parallel resistors can be written in two algebraically equivalent ways:

; Z = R1 * R2 / (R1 * R2)
; Z = 1 / (1 / R1 * 1 / R2)

; He has written the following two programs, each of which computes
; the parallel-resistors formula differently:
;
; (define (par1 r1 r2)
;   (div-interval
;    (mul-interval r1 r2)
;    (add-interval r1 r2)))
;
; (define (par2 r1 r2)
;   (let ((one (make-interval 1 1)))
;     (div-interval
;      one
;      (add-interval
;       (div-interval one r1)
;       (div-interval one r2)))))
;
; Lem complains that Alyssa’s program gives different answers for the two ways of computing.
; This is a serious complaint.

(defn par1
  [r1 r2]
  (m/div-interval (m/mul-interval r1 r2)
                  (m/add-interval r1 r2)))

(defn par2
  [r1 r2]
  (let [one (m/make-interval 1 1)]
    (m/div-interval one (m/add-interval
                          (m/div-interval one r1)
                          (m/div-interval one r2)))))