With this version of use_str:

sub use_str
{
    my $re = qr/^1\d2\d3\d4\d5\d6\d7\d8\d900$/;

    for (my $n = 1_010_101_030; $n <= 1_389_026_623; )
    {
        # stringify the qr regex
        my $str = "$re";
        my $s  = $n * $n;
        return   $n if $s =~ /$str/; # recompiled each time I guess?
           $n += 40;
           $s  = $n * $n;
        return   $n if $s =~ /$str/;
           $n += 60;
    }

    die;
}
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I get:

Benchmark: timing 5 iterations of use_qr, use_re, use_str...
    use_qr: 33 wallclock secs (33.62 usr +  0.00 sys = 33.62 CPU) @  0
+.15/s (n=5)
    use_re: 18 wallclock secs (17.14 usr +  0.00 sys = 17.14 CPU) @  0
+.29/s (n=5)
   use_str: 25 wallclock secs (24.99 usr +  0.00 sys = 24.99 CPU) @  0
+.20/s (n=5)
        s/iter  use_qr use_str  use_re
use_qr    6.72      --    -26%    -49%
use_str   5.00     35%      --    -31%
use_re    3.43     96%     46%      --

Appuyez sur une touche pour continuer...
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So this looks like perl is doing even worse with qr than it would by recompiling the stringified version on each iteration (unless I'm missing some optimization, but I tried adding dummy logic like rand(100) < 100 to prevent perl from noticing that the expression are constants, and didn't see significant changes)?

Edit: perl v5.20 here BTW