$ perl -e '
    my $x = $ARGV[0];
    $x =~ s/(`[^`]+`)/chomp(my $y = eval $1); $y/eg;
    print "$x\n";
' 'DMY_`date +%d%m%Y`_MY_`date +%m%Y`_Y_`date +%Y`.log'
DMY_21122019_MY_122019_Y_2019.log