my @in = qw(nc01123.log
            nc02123.log
            nc03123.log);
my $year = '0';
my $month = '2';
@in = grep { /^nc$year$month.*\.log$/ } @in;
print "@in\n";
__END__

Try zero: The nested sub block was hard to read so this didn't yield too much.
perl -MO=Concise test.pl

Try one: This makes it look like the regex is compiled anew each time.
perl -MO=Concise,-exec test.pl

Try two: This looks like the regex is compiled only once. Or maybe debug just <i>dumps</i> it once.
use re 'debug';