sub ikegami3x {
    local $_ = ":$_[0]:";

    my $parts = tr/:/:/ - 2; # take 2 here instead of -1 later

    my $re = '(?{ "" })'
           . '(:[^:]*)(?=:)(?{ $^R . $^N })'
           . '(?:.*(:[^:]*)(?=:)(?{ $^R . $^N })' x $parts
           . ')?' x $parts
           . '(?{ push @rv, substr($^R, 1) })'
           . '(?!)';

    { use re 'eval'; $re = qr/$re/; }

    local our @rv;
    /$re/;
    return @rv;
}

##</code><code>##

sub rhesa2 {
    my @kw = split /:/, $_[0];
    map {
        my @ar;
        my $t = 0; # initialize $t
        do {
            ($_ & 1) and push @ar, $kw[$t];
            $t++;
        } while ($_ >>= 1);
        join ':', @ar;
    } ( 1 .. 2**@kw - 1 );
}

##</code><code>##

source: horse:cow:dog:cat
             Rate  ruzam  ikegami3  ikegami2  ikegami3x  rhesa2  rhesa
ruzam      4620/s     --     -61%      -61%       -61%    -66%   -66%
ikegami3  11764/s   155%       --       -0%        -1%    -12%   -14%
ikegami2  11819/s   156%       0%        --        -1%    -12%   -13%
ikegami3x 11935/s   158%       1%        1%         --    -11%   -13%
rhesa2    13444/s   191%      14%       14%        13%      --    -2%
rhesa     13657/s   196%      16%       16%        14%      2%     --

source: horse
              Rate ikegami3  ikegami3x  ruzam  ikegami2  rhesa  rhesa2
ikegami3   40841/s      --        -1%    -37%     -62%   -64%    -72%
ikegami3x  41226/s      1%         --    -37%     -62%   -64%    -72%
ruzam      65317/s     60%        58%      --     -39%   -43%    -55%
ikegami2  107178/s    162%       160%     64%       --    -6%    -26%
rhesa     114470/s    180%       178%     75%       7%     --    -21%
rhesa2    145232/s    256%       252%    122%      36%    27%      --

source: horse:cat
             Rate  ruzam  ikegami3  ikegami3x  ikegami2  rhesa  rhesa2
ruzam     26853/s     --      -2%        -7%      -48%   -53%    -58%
ikegami3  27324/s     2%       --        -5%      -47%   -52%    -58%
ikegami3x 28732/s     7%       5%         --      -45%   -50%    -55%
ikegami2  51965/s    94%      90%        81%        --    -9%    -19%
rhesa     57233/s   113%     109%        99%       10%     --    -11%
rhesa2    64472/s   140%     136%       124%       24%    13%      --

source: horse:cow:cat
             Rate  ruzam  ikegami3 ikegami3x  ikegami2  rhesa  rhesa2
ruzam     10772/s     --     -41%      -42%      -58%   -61%    -64%
ikegami3  18305/s    70%       --       -1%      -28%   -33%    -38%
ikegami3x 18436/s    71%       1%        --      -27%   -33%    -38%
ikegami2  25353/s   135%      39%       38%        --    -7%    -15%
rhesa     27363/s   154%      49%       48%        8%     --     -8%
rhesa2    29753/s   176%      63%       61%       17%     9%      --

source: horse:cow:dog:cat:mouse
            Rate  ruzam  rhesa  ikegami2  rhesa2  ikegami3x  ikegami3
ruzam     1632/s     --  -67%      -68%    -73%       -75%      -75%
rhesa     5021/s   208%    --       -3%    -17%       -24%      -24%
ikegami2  5159/s   216%    3%        --    -14%       -22%      -22%
rhesa2    6023/s   269%   20%       17%      --        -9%       -9%
ikegami3x 6614/s   305%   32%       28%     10%         --       -0%
ikegami3  6634/s   307%   32%       29%     10%         0%        --