gistfile1.scm

(define (good-enough? guess x)
  (< (abs (- (square guess) x)) 0.001))

;; The good-enough? test used in computing square roots will not be
;; very effective for finding the square roots of very small numbers. Explain.
;;
;; good-enough? is not effective for small numbers because the square
;; of a small number minus the number quickly becomes less than 0.001.

(sqrt 0.00001)
=> .031356
;; correct answer is 0.003162

;; Also, in real computers, arithmetic operations are almost always
;; performed with limited precision. This makes our test inadequate
;; for very large numbers. Explain.
;;
;; good-enough? is not effective for very large numbers because the lack
;; of precision prevents the difference between the two numbers from ever
;; getting small enough.

(sqrt 100000000000000000000000000000000000000000000000000000000000000000)
=> NEVER RETURNS
;; correct answer is 3.16227766016838e+32