; Exercise 1.7. The good-enough? test used in computing square roots will not be very effective for

; finding the square roots of very small numbers. Also, in real computers, arithmetic operations are almost

; always performed with limited precision. This makes our test inadequate for very large numbers. Explain

; these statements, with examples showing how the test fails for small and large numbers. An alternative

; strategy for implementing good-enough? is to watch how guess changes from one iteration to the next and

; to stop when the change is a very small fraction of the guess. Design a square-root procedure that uses

; this kind of end test. Does this work better for small and large numbers?

(define (sqrt-iter guess x)

(if (good-enough? guess x)

guess

(sqrt-iter (improve guess x)

x)))

(define (improve guess x)

(average guess (/ x guess)))

(define (average x y)

(/ (+ x y) 2))

(define (square x) (* x x))

(define (good-enough? guess x)

(< (/ (abs (- (square guess) x)) x) 0.001))

(define (sqrt x)

(sqrt-iter 1.0 x))

(display (sqrt 4)) (newline)

(display (sqrt 0.0004)) (newline)

; This works better for small numbers

2 days ago

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