PHPMailer で「SMTP connect() が失敗しました」エラーが表示されるのはなぜですか?

<code class="php">require "class.phpmailer.php";
$mail = new PHPMailer(); 
$mail->IsSMTP();                              // send via SMTP
$mail->Host = "tls://smtp.gmail.com";
$mail->SMTPAuth = true;                       // turn on SMTP authentication
$mail->Username = "[email protected]";        // SMTP username
$mail->Password = "mypassword";               // SMTP password
$webmaster_email = "[email protected]";       //Reply to this email ID
$email="[email protected]";                // Recipients email ID
$name="My Name";                              // Recipient's name
$mail->From = $webmaster_email;
$mail->Port = 587;
$mail->FromName = "My Name";
$mail->AddAddress($email,$name);
$mail->AddReplyTo($webmaster_email,"My Name");
$mail->WordWrap = 50;                         // set word wrap
$mail->IsHTML(true);                          // send as HTML
$mail->Subject = "subject";
$mail->Body = "Hi,
This is the HTML BODY ";                      //HTML Body 
$mail->AltBody = "This is the body when user views in plain text format"; //Text Body 

if(!$mail->Send())
{
echo "Mailer Error: " . $mail->ErrorInfo;
}
else
{
echo "Message has been sent";
}
?></code>