User Registration Front End WordPress with Ajax

functions.php

<?php 
add_action('wp_ajax_register_user_front_end', 'register_user_front_end', 0);
add_action('wp_ajax_nopriv_register_user_front_end', 'register_user_front_end');
function register_user_front_end() {
	  $new_user_name = stripcslashes($_POST['new_user_name']);
	  $new_user_email = stripcslashes($_POST['new_user_email']);
	  $new_user_password = $_POST['new_user_password'];
	  $user_nice_name = strtolower($_POST['new_user_email']);
	  $user_data = array(
	      'user_login' => $new_user_name,
	      'user_email' => $new_user_email,
	      'user_pass' => $new_user_password,
	      'user_nicename' => $user_nice_name,
	      'display_name' => $new_user_first_name,
	      'role' => 'subscriber'
	  	);
	  $user_id = wp_insert_user($user_data);
	  	if (!is_wp_error($user_id)) {
	      echo 'we have Created an account for you.';
	  	} else {
	    	if (isset($user_id->errors['empty_user_login'])) {
	          $notice_key = 'User Name and Email are mandatory';
	          echo $notice_key;
	      	} elseif (isset($user_id->errors['existing_user_login'])) {
	          echo'User name already exixts.';
	      	} else {
	          echo'Error Occured please fill up the sign up form carefully.';
	      	}
	  	}
	die;
}

index.html

    <p class="register-message" style="display:none"></p>
    <form action="#" method="POST" name="register-form" class="register-form">
      <fieldset> 
          <label><i class="fa fa-file-text-o"></i> Register Form</label>
          <input type="text"  name="new_user_name" placeholder="Username" id="new-username">
          <input type="email"  name="new_user_email" placeholder="Email address" id="new-useremail">
          <input type="password"  name="new_user_password" placeholder="Password" id="new-userpassword">
          <input type="password"  name="re-pwd" placeholder="Re-enter Password" id="re-pwd">
          <input type="submit"  class="button" id="register-button" value="Register" >
      </fieldset>
    </form> 
     

    <script type="text/javascript">
      jQuery('#register-button').on('click',function(e){
        e.preventDefault();
        var newUserName = jQuery('#new-username').val();
        var newUserEmail = jQuery('#new-useremail').val();
        var newUserPassword = jQuery('#new-userpassword').val();
        jQuery.ajax({
          type:"POST",
          url:"<?php echo admin_url('admin-ajax.php'); ?>",
          data: {
            action: "register_user_front_end",
            new_user_name : newUserName,
            new_user_email : newUserEmail,
            new_user_password : newUserPassword
          },
          success: function(results){
            console.log(results);
            jQuery('.register-message').text(results).show();
          },
          error: function(results) {

          }
        });
      });
    </script>