SICP Tasks

newton-cube-square-root.scm

(define (square a)
	(* a a))

(define (cube a)
	(* a a a))

(define (abs a)
	(if (< a 0) (- a) a))

(define (average a b)
	(/ (+ a b) 2))

(define (until pred impr init)
	(define (until-iter guess)
		(if (pred guess)
		    guess
		    (until-iter (impr guess))))
	(until-iter init))

(define (sqrt x)
	
	(define (good-enough? guess)
		(< (abs (- (square guess) x)) 0.001))
	
	(define (improve guess)
		(average (/ x guess) guess))

	(until good-enough? improve 1.0))

(define (cbrt x)

	(define (good-enough? guess)
		(< (abs (- (cube guess) x)) 0.001))
	
	(define (improve guess)
		(/ (+ (/ x (square guess)) (* 2 guess)) 3))
	
	(until good-enough? improve 1.0))