I am studying SICP and wrote two procedures to compute the sum of 1/n^2, the first generating a recursive process and the second generating an iterative process :
(define (sum-rec a b)
(if (> a b)
0
(exact->inexact (+ (/ 1 (* a a)) (sum-rec (1+ a) b)))))
(define (sum-it a b)
(define (sum_iter a tot)
(if (> a b)
tot
(sum_iter (1+ a) (+ (/ 1 (* a a)) tot))))
(exact->inexact (sum_iter a 0)))
I tested that both procedures give exactly the same results when called with small values of b, and that the result is approaching $pi^2/6$ as b gets larger, as expected.
But surprisingly, calling (sum-rec 1 250000) is almost instantaneous whereas calling (sum-it 1 250000) takes forever.
Is there an explanation for that?
As was mentioned in the comments, sum-it in its present form is adding numbers using exact arithmetic, which is slower than the inexact arithmetic being used in sum-rec. To do an equivalent comparison, this is how you should implement it:
(define (sum-it a b)
(define (sum_iter a tot)
(if (> a b)
tot
(sum_iter (1+ a) (+ (/ 1.0 (* a a)) tot))))
(sum_iter a 0))
Notice that replacing the 1 with a 1.0 forces the interpreter to use inexact arithmetic. Now this will return immediately:
(sum-it 1 250000)
=> 1.6449300668562465