Although proper tail recursion does tend to make programs run faster, proper tail recursion is really about space efficiency: Properly tail recursive implementations of a programming language are asymptotically more space-efficient than implementations that are not properly tail recursive.

That is easy to demonstrate.

      ;;; Given two non-negative integers, returns their sum.
      
      (define (sum m n)
        (if (= m 0)
            n
            (sum (- m 1) (+ n 1))))
    

In Scheme, (sum 1000000 1) runs in constant space and returns 1000001.

Implementations of Java are not properly tail recursive, and seldom attempt tail call optimization, so giving m and n as inputs to the following method takes Θ(m) stack space. With m = 1000000, you'll probably get a stack overflow.

          // Given two non-negative integers, returns their sum.
      
          static int sum (int m, int n) {
              if (m == 0)
                  return n;
              else
                  return sum (m - 1, n + 1);
          }