Daniel-Nikpayuk_SICP-Solutions/Chapter 1/1.1/exercise-1.08/exercise.lsp
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;; Copyright 2015 Daniel Nikpayuk
;;
;; This file is part of SICP Solutions.
;;
;; SICP Solutions is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License
;; as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
;;
;; SICP Solutions is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty
;; of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
;;
;; You should have received a copy of the GNU General Public License along with SICP Solutions. If not, see
;; <http://www.gnu.org/licenses/>.
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(define (cube x)
  (* x x x))

(define (improve guess x)
  (/ (+ (/ x (square guess)) (* 2 guess)) 3))

(define (good-enough? guess0 guess1)
  (< (abs (- guess0 guess1)) (* 0.001 guess0)))

(define (cbrt-iter guess0 guess1 x)
  (if (good-enough? guess0 guess1)
      guess0
      (cbrt-iter guess1 (improve guess1 x)
                 x)))

(define (cbrt x)
  (cbrt-iter 1.0 (improve 1.0 x) x))
