Even faster than index() or a regex -- I would imagine -- would be substr() and eq together.

When imagine when you can Benchmark?

use Benchmark 'cmpthese';
my $str1 = 'foobarbazqux';
my $str2 = 'foobar';
my $str2len = length $str2;

cmpthese (3e6, {
  regex   => sub { $str1 =~ /\Q$str2/; },
  regex2  => sub { $str1 =~ /\Q$str2/o; },  ## probably useless test, 
+see japhy's comment below
  index   => sub { index $str1, $str2; },
  substr  => sub { $str2 eq substr $str1, 0, length $str2; },
  substr2 => sub { $str2 eq substr $str1, 0, $str2len; },
});
__END__
             Rate   regex  regex2  substr substr2   index
regex   1063830/s      --    -13%    -25%    -43%    -72%
regex2  1229508/s     16%      --    -14%    -34%    -68%
substr  1421801/s     34%     16%      --    -23%    -63%
substr2 1851852/s     74%     51%     30%      --    -51%
index   3797468/s    257%    209%    167%    105%      --
[download]

The index solution is clearly superior to the others. It's interesting to see the improvements of regex2 and substr2 over their unoptimized counterparts.

Update: I forgot that the OP was matching at the beginning of the string. This is a better benchmark:

use Benchmark 'cmpthese';
my $str1 = 'foobarbazqux';
my $str2 = 'foobar';
my $str2len = length $str2;

cmpthese (3e6, {
  regex   => sub { $str1 =~ /^\Q$str2/; },
  index   => sub { 0 == index $str1, $str2; },
  substr  => sub { $str2 eq substr $str1, 0, length $str2; },
  substr2 => sub { $str2 eq substr $str1, 0, $str2len; },
});
__END__
             Rate   regex  substr substr2   index
regex    671141/s      --    -59%    -65%    -71%
substr  1630435/s    143%      --    -16%    -30%
substr2 1935484/s    188%     19%      --    -17%
index   2343750/s    249%     44%     21%      --
[download]

I wouldn't bring /o into the equation. It makes a regex "sterile" which wouldn't be helpful if this were in a function where the strings are arguments.

You haven't provided any data for failing cases. The further the smaller string is from the beginning of the bigger string, the slower index() will be.

---

Jeff japhy Pinyan, P.L., P.M., P.O.D, X.S.: Perl, regex, and perl hacker
How can we ever be the sold short or the cheated, we who for every service have long ago been overpaid? ~~ Meister Eckhart