You're comparing assinging a string of 4 characters to assigning a string of 100 characters. I don't see the relevance to the topic at hand. Here's a more relevant benchmarks.

Compile-time difference

          Rate single double
single 30027/s     --    -0%
double 30160/s     0%     --

Run-time difference

            Rate single double
single 5968932/s     --   -13%
double 6893402/s    15%     --

            Rate double single
double 6218672/s     --   -12%
single 7062848/s    14%     --
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I'm getting lots of variation in the run-time results. The differences are probably due to external sources. Since the opcodes are the same, they should take the same amount of time.

use strict;
use warnings;

use Benchmark qw( cmpthese );

my $as = 'a' x 100;

sub c_dq {
  eval "\$a = \"$as\";";
}

sub c_sq {
  eval "\$a = '$as';";
}

eval "sub r_dq { \$a = \"$as\"; }";

eval "sub r_sq { \$a = '$as'; }";

print("Compile-time difference\n");

cmpthese(-3, {
   double => \&c_dq,
   single => \&c_sq,
});

print("Run-time difference\n");

cmpthese(-3, {
   double => \&r_dq,
   single => \&r_sq,
});
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