How to compare passwords the correct way? wp_hash_password

I seems that wordpress encrypt the password of the user in a MD5 custom way. As you can see in the code below i am trying to compare the password out of the database with the one the user entered.

I encrypting the posted password with md5 and wp_hash_password();
note that one each refresh or another formpost the posted md5 and wp_hash_password(); gets a random output.

My problem is now that i can’t compare the passes. Anyone got a idea?

<?php 

include_once($_SERVER['DOCUMENT_ROOT'].'/wp-config.php');
include_once($_SERVER['DOCUMENT_ROOT'].'/wp-load.php');
include_once($_SERVER['DOCUMENT_ROOT'].'/wp-includes/wp-db.php');

global $userdata;
global $wpdb; 

//get the posted values

$posted_username = $_POST['username'];
$posted_password = $_POST['password'];

$user_name = htmlspecialchars($posted_username,ENT_QUOTES);

$pass_word = wp_hash_password($posted_password);

$pass_md5 = md5($posted_password);

$pass = $pass_word;

$userinfo = get_userdatabylogin($user_name);

if ( $pass == $userinfo->user_pass){

		echo "yes";

	} else 

		echo "no<br />:";

echo $pass;
echo '<br />:';
echo $userinfo->user_pass;
echo '<br />:';
echo $userinfo->ID;
echo '<br />:';
echo $userinfo->user_login;
echo '<br />:';
echo $pass_md5;
echo '<br />:';
echo wp_hash_password('mypassword');

?>

Returns the following values

no
:$P$BJhGR7TPd771cFb6UFVSknys.MDjBw.
:$P$B7g6c9b3YavlDCT41/1wNWxUqN5E4q1
:1
:myusername
:8684854737c96012f1b6640fa1edf69d
:$P$B0T9SE3Cnd3NM2iEPFJ.SxwqSCBFR8/

The random values on a refresh/rePOST

no
:$P$Bhjs6fejE8OOb2P.jEFa3VbD0BLpb40
:$P$B7g6c9b3YavlDCT41/1wNWxUqN5E4q1
:1
:myusername
:8684854737c96012f1b6640fa1edf69d
:$P$BtWdkKKaw5DyXQmZ12CkX5ljyvZDv80