My man pages say that %e is the same as %d, i.e., the day of the month.(Update: I need glasses...OP is %s not %e) That said, you don't have to 'parse' an epoch, you just pass it to new():

use strict;
use warnings;
use Time::Piece;

my $e = time();
my $t = Time::Piece->new($e);
print Time::Piece->VERSION, "\n";

print "Input $e\n";
print "Output ".$t->epoch(), "\n";
print $t, "\n";
print $t->strftime, "\n";
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