<form role="search" method="get" id="searchform" action="<?php echo home_url( '/' ); ?>">
    <div>
        <input type="text" value="" name="s" id="s" placeholder="Search" />
        <!-- <input type="submit" class="btn btn-live s_widget_btn" id="searchsubmit" value="Search" /> -->
    </div>
</form>