It also helps to have a repl-loop so you can quickly try out how long the concatenation of 1..300000 takes and correct the number to a better approximation in a few steps.

Well, that's what I would probably do if I had your skills and that interpreter. Still I'm interested in elegant and smart solutions that fit both in current Perl and in the much more interesting Perl 6 with its additional degrees of freedom. Of course Perl will never be an entirely mathematically oriented language, but if we can "improve" the situation, ain't it good anyway?

BTW: sorry for replying so late. I've had and I'm still having very big troubles in real life which prevent me from writing all that I would want in virtual one. I was reminded of this long postponed followup by Re^2: [Perl 6] Even more freedom for custom operators?.