(define (product term a next b)
  (define (prod-iter a result)
    (if (> a b)
        result
        (prod-iter (next a) (* result (term a)))))
  (prod-iter a 1))

(define (id n) n)

(define (inc n) (+ n 1))

(define (fact n)
  (product id 1 inc n))

(define (approx-pi n)
  (define (term-even a)
    (* 2 a))
  (define (term-odd a)
    (+ 1 (* 2 a)))
  (* 4.0
     (/ (* (product term-even 1 inc n) (product term-even 2 inc (+ 1 n)))
        (square (product term-odd 1 inc n)))))

;1 ]=> (approx-pi 1000)
;
;Value: 3.142377365093878
;
;1 ]=> (approx-pi 10000)
;
;Value: 3.1416711865344635
;
;1 ]=> (approx-pi 100000)
;
; -- time passes --
;
;Value: 3.1416005075027056
;