Why would adding a line of computation decrease runtime?

Question

When testing an answer to one of my related questions, I wrote this:

public static long timeDouble(int iters) {
    long start = System.currentTimeMillis();
    for (; iters >=0; iters--) {
        double a = 1.2, b = 2.246, c = 4.4924, d = 8.98488, e = 17.969772;
        a = Math.sqrt(a);
        b = Math.cos(b);
        c = Math.sin(c);
        d = Math.tan(d);
        e = a + b - c * d / (e + 1);
        e = Math.pow(e, e);
    }
    return System.currentTimeMillis() - start;
}

This method's run time was an average of 414ms (using 1000000 iterations). However, something possessed me to add this line:

e = e + d - c * b / (a + 1);

immediately before e = Math.pow(e, e); With the addition of this line, the time for calculating this method dropped to an average of 206 ms (using the same test conditions).

What is causing this?

Maybe the value of `e` is decreased by that equation, and then `Math.pow(e, e)` will take less time to execute. — Eng.Fouad, Jul 11 '12 at 16:24
It's probably due to the fact that Math.pow(e, e) is using less processor cycles, perhaps due to the fact that e is smaller. — Sam I am says Reinstate Monica, Jul 11 '12 at 16:25
The above posters are probably correct, but I'd generally steer away from this kind of microbenchmarking, it has quite a few pitfalls. http://www.kdgregory.com/index.php?page=java.microBenchmark — Vala, Jul 11 '12 at 16:29

score 3 · Accepted Answer · answered Jul 11 '12 at 16:28

The values in the loop are constant, they don't depend on iters. and therefore the values are the same all the time.

    double a = 1.2, b = 2.246, c = 4.4924, d = 8.98488, e = 17.969772;
    a = Math.sqrt(a);
    b = Math.cos(b);
    c = Math.sin(c);
    d = Math.tan(d);
    e = a + b - c * d / (e + 1);
    e = Math.pow(e, e);

In the first version you were calculating e to be the value 17.969772 ^ 17.969772. In the second you are calculating e to be the value 0.69761863561124537 ^ 0.69761863561124537. This is (by your own evidence) easier to computer.

Why would adding a line of computation decrease runtime?

1 Answers1