some solutions for MIT Press's "structure and interpretation of computer programs", I guess
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(define (square x) (* x x))
(define (cube x) (* x x x))
;; (x / y ^ 2 + 2y) / 3
(define (improve y x)
(/ (+ (/ x (square y)) (* 2 y)) 3))
(define (good-enough? y old)
(< (abs (- y old)) 0.001))
(define (cbrt-iter y old x)
(if (good-enough? y old)
y
(cbrt-iter (improve y x) y x)))
(define (my-cbrt x)
(cbrt-iter 1.0 x x))
(display (my-cbrt 9))