sicp 2.57

#lang racket
(define (deriv exp var)
  (cond ((number? exp) 0)
        ((variable? exp)
         (if (same-variable? exp var) 1 0))
        ((sum? exp)
         (make-sum (deriv (addend exp) var)
                   (deriv (augend exp) var)))
        ((product? exp)
         (make-sum
           (make-product (multiplier exp)
                         (deriv (multiplicand exp) var))
           (make-product (deriv (multiplier exp) var)
                         (multiplicand exp))))
        (else
         (error "unknown expression type -- DERIV" exp))))

(define (variable? x) (symbol? x))

(define (same-variable? v1 v2)
  (and (variable? v1) (variable? v2) (eq? v1 v2)))

(define (make-sum a1 a2)
  (cond ((=number? a1 0) a2)
        ((=number? a2 0) a1)
        ((and (number? a1) (number? a2)) (+ a1 a2))
        (else (list '+ a1 a2))))

(define (=number? exp num)
  (and (number? exp) (= exp num)))

(define (make-product m1 m2)
  (cond ((or (=number? m1 0) (=number? m2 0)) 0)
        ((=number? m1 1) m2)
        ((=number? m2 1) m1)
        ((and (number? m1) (number? m2)) (* m1 m2))
        (else (list '* m1 m2))))

(define (sum? x)
  (and (pair? x) (eq? (car x) '+)))

(define (addend s)
  (cond ((equal? (cdr s) '()) 0)
        (else (cadr s))))

(define (augend s)
  (cond ((equal? (cdr s) '()) 0)
        (else (cons (car s) (cddr s)))))

(define (product? x)
  (and (pair? x) (eq? (car x) '*)))

(define (multiplier p)
  (cond ((equal? (cdr p) '()) 1)
        (else  (cadr p))))

(define (multiplicand p)
  (cond ((equal? (length  (cddr p)) 1) (caddr p))
        (else (cons (car p) (cddr p)))))

(deriv '(+ (+ x 3) x) 'x)
(deriv '(+  (+ x x) (+ x x)) 'x)
(deriv '(+  (+ (+ x x) x) x) 'x)
(deriv '(+  x x x) 'x)
;;(deriv '(+  x x x (+ x 3)) 'x)
(deriv '(*  x x ) 'x)
(deriv '(*  x x x) 'x)
(deriv '(*  (* x y) x) 'x)
(deriv '(*  x y x) 'x)

(deriv '(* (* x y) (+ x 3)) 'x)
;;'(+ (* x y) (* y (+ x 3)))

(equal? (deriv '(* x y (+ x 3)) 'x) (deriv '(* (* x y) (+ x 3)) 'x))