結論

gistfile1.pl

#!/usr/bin/env perl
use strict;
use warnings;
use utf8;
use feature 'say';
use Benchmark qw(cmpthese);

say $];

my $pattern = '((?:(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\.){3}(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?))';
my $regexp = qr/$pattern/;
my $ipv4 = '192.168.1.1';

cmpthese(0, +{
    'reref_expand_pattern' => sub {
        $ipv4 =~ qr/$pattern/;
    },
    'reref_static' => sub {
        $ipv4 =~ qr/((?:(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\.){3}(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?))/;
    },
    'expand_reref' => sub {
        $ipv4 =~ /$regexp/;
    },
    'precompile' => sub {
        $ipv4 =~ $regexp;
    },
    'expand_pattern' => sub {
        $ipv4 =~ /$pattern/;
    },
    'static' => sub {
        $ipv4 =~ /((?:(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)\.){3}(?:25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?))/;
    },
});

ふと思い立って色んな長さのパターンで試してみた

5倍の長さ（上記パターンの5回繰り返し）

                           Rate reref_expand_pattern reref_static expand_reref precompile expand_pattern static
reref_expand_pattern  1031053/s                   --          -5%         -69%       -72%           -92%   -97%
reref_static          1082539/s                   5%           --         -68%       -71%           -92%   -97%
expand_reref          3352499/s                 225%         210%           --       -10%           -74%   -91%
precompile            3729822/s                 262%         245%          11%         --           -71%   -90%
expand_pattern       12923405/s                1153%        1094%         285%       246%             --   -65%
static               37147799/s                3503%        3332%        1008%       896%           187%     --

ipv4の最初の数字のみ /(25[0-5]|2[0-4][0-9]|[01]?[0-9][0-9]?)/

                          Rate reref_expand_pattern reref_static precompile expand_reref expand_pattern static
reref_expand_pattern  809465/s                   --          -9%       -49%         -50%           -74%   -76%
reref_static          891487/s                  10%           --       -44%         -45%           -71%   -74%
precompile           1582768/s                  96%          78%         --          -2%           -48%   -54%
expand_reref         1613850/s                  99%          81%         2%           --           -47%   -53%
expand_pattern       3055255/s                 277%         243%        93%          89%             --   -11%
static               3440637/s                 325%         286%       117%         113%            13%     --

1文字のみ /1/

                           Rate reref_expand_pattern reref_static precompile expand_reref expand_pattern static
reref_expand_pattern  1037153/s                   --          -6%       -63%         -64%           -90%   -92%
reref_static          1099748/s                   6%           --       -61%         -62%           -89%   -92%
precompile            2802480/s                 170%         155%         --          -2%           -72%   -79%
expand_reref          2861048/s                 176%         160%         2%           --           -72%   -79%
expand_pattern       10190294/s                 883%         827%       264%         256%             --   -25%
static               13508011/s                1202%        1128%       382%         372%            33%     --

全方位的にベタ書き最強でしたとさ。