With corrected versions of yours and mine, plus ikegami's suggested alteration of mine:

use strict; 
use warnings;
use Benchmark 'cmpthese';
cmpthese( -2, {
holli => sub {
    $_ = "fox comes and fox goes into forest";
    s/(fox.+)?(fox.+?forest)/${1}the $2/;
},
Roy => sub {
    $_ = "fox comes and fox goes into forest";
    s/(?=fox(?:(?!fox).)*forest)/the /;
},
ikegami => sub {
    $_ = "fox comes and fox goes into forest";
    s/(fox(?:(?!fox).)*forest)/the $1/;
},
});
[download]

           Rate ikegami   holli     Roy
ikegami 34714/s      --     -2%    -27%
holli   35541/s      2%      --    -25%
Roy     47659/s     37%     34%      --
[download]