Map has lower overhead than many other list changing algorithms... this is mostly because it uses better, faster, fewer temporary variables. Lets comapare using our good old friend Devel::OpProf.

#!/usr/bin/perl
use warnings;
use strict;
use Devel::OpProf qw'profile print_stats zero_stats';

my @source = ( 1..10_000 );
my @dest = ();

#measure the map
profile(1);
@dest = map { $_ * 10 } @source;
profile(0);

print "*** map ***\n";
print_stats();
zero_stats();
@dest = ();

#measure the foreach
profile(1);
foreach(@source){
    @dest = $_ * 10;
}
profile(0);

print "\n*** foreach ***\n";
print_stats();
zero_stats();
@dest = ();

#measure the for
profile(1);
push @dest, $_ * 10 for @source;

profile(0);

print "\n*** for ***\n";
print_stats();
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The output:

*** map ***
null operation           10005
constant item            10001
scalar variable          10000
map iterator             10000
multiplication (*)       10000
block                    10000
pushmark                 4
next statement           2
private array            2
list assignment          1
map                      1
subroutine entry         1
glob value               1

*** foreach ***
null operation           20005
pushmark                 20002
next statement           20002
glob value               10002
logical and (&&)         10001
private array            10001
constant item            10001
foreach loop iterator    10001
iteration finalizer      10000
multiplication (*)       10000
scalar dereference       10000
list assignment          10000
foreach loop entry       1
subroutine entry         1
loop exit                1

*** for ***
next statement           10003
glob value               10002
pushmark                 10002
logical and (&&)         10001
private array            10001
constant item            10001
foreach loop iterator    10001
multiplication (*)       10000
push                     10000
iteration finalizer      10000
scalar dereference       10000
null operation           5
foreach loop entry       1
subroutine entry         1
loop exit                1

So we see that, a map has less action than a foreach, and stuffing the for in the push is almost as good as a map, and with many of the same operations going on.
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