while (<STDIN>)
{
    if (/(\d+) matches\)/)
    {
        # keep this in a list we'll sort later
        push @list, [ $1, $_ ];
    }
    else
    {
        # same case as before, write it to the log
        print LOG;
    }
}
# Now print out the list we built before in sorted order
foreach (sort { $a->[0] <=> $b->[0] } @list )
{
    print $_->[1];
}