I improved the SQL, this one here is a bit faster. I also include below changes to your test program, as lines to be added. The DBI connect will inevitably need some tweaking, depending on host machine.

use DBI;

#my $dbh = DBI->connect or die "hm - $@\n"; # easier when ENV vars are
+ set
my $dbh  = DBI->connect('dbi:Pg:', "app_user1", "P4ss_W0rd1") or die "
+meh - no db connection - $@\n" ;

# two test lines:

is _sql()     , $union;

"SQL/Pg"   => \&_sql,

# and the statement itself
sub _sql  { 

  return $dbh->selectrow_arrayref("

select array_to_string( array(
 select lower(isect) || '-' || upper(isect)-1 from(
  select
      ('['||replace(unnest(string_to_array('$TM_part1', ',')), '-', ',
+')||']')::int4range
    * ('['||replace(unnest(string_to_array('$TM_part2', ',')), '-', ',
+')||']')::int4range 
 ) as h(isect)
), ',')

")->[0] ;

}
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and this is the new result:

              Rate     Span     Perl   SQL/Pg     Pair oneliner
Span        8373/s       --     -57%     -68%     -86%    -100%
Perl       19261/s     130%       --     -27%     -69%    -100%
SQL/Pg     26397/s     215%      37%       --     -57%    -100%
Pair       61443/s     634%     219%     133%       --     -99%
oneliner 5644800/s   67313%   29207%   21284%    9087%       --
[download]