timethese( 100, {
 'better' => sub {
     while ($mmap =~ m/(?:\A|\n)(.*$pat.*\n)/omg) {
     }
 },
 'tye1' => sub {
     while ($mmap =~ m/(?:\A|(?<=\n))(.*$pat.*\n)/omg) {
     }
 },
 'tye2' => sub {
     while ($mmap =~ m/(?:\A|(?<![^\n]))(.*$pat.*\n)/omg) {
     }
 },
})
__END__
Benchmark: timing 100 iterations of better, tye1, tye2...
    better: 11 wallclock secs (10.61 usr +  0.00 sys = 10.61 CPU) @  9.43/s (n=100)
      tye1: 13 wallclock secs (12.37 usr +  0.00 sys = 12.37 CPU) @  8.08/s (n=100)
      tye2: 14 wallclock secs (14.16 usr +  0.00 sys = 14.16 CPU) @  7.06/s (n=100)