🚀 go-pugleaf

In article <1992Nov13.141300.3528@clark.dgim.doc.ca> don@mars.dgrc.doc.ca writes:
>I believe correct results are far more important to Herman than the wrong answer
>3 times as quickly.  Therefore the folks arguing over which is more important,
>correctness or speed, are also wasting bandwidth.

Hi,
	There is one comment I'd like to make on this, which is that no one
who's mentioned correctness and speed has discussed it properly, which is to
say, in terms of the expected running time to find the correct answer.

If there exists an algorithm which runs 6 times as fast as Herman's current
algorithm, but gives a wrong answer 1/3 of the time, then he might expect to
have to run it 3 times for a correct answer, which is still twice as fast as
his current algorithm.  Since factorization is easy to check, a wrong answer
would not impose any serious time costs in that event.

So you see, you should not argue over which is better, correctness or speed,
without considering which type of algorithm you can expect to give you the
right answer in which amount of time.

I expect Herman already knows this, as most people who work with numeric
algorithms of that sort are familiar with probabilistic algorithms and
analyzing their running time.

Ted