.table-cell {
display: table-cell;
vertical-align: middle;
}
.fill-width {
width:100%;
}<nav class="navbar navbar-dark bg-inverse">
<a class="navbar-brand" href="#">Navbar</a>
<ul class="nav navbar-nav pull-xs-left">
<li class="nav-item active">
<a class="nav-link" href="#">Home <span class="sr-only">(current)</span></a>
</li>
<li class="nav-item">
<a class="nav-link" href="#">Features</a>
</li>
<li class="nav-item">
<a class="nav-link" href="#">Pricing</a>
</li>
<li class="nav-item">
<a class="nav-link" href="#">About</a>
</li>
</ul>
<ul class="nav navbar-nav pull-xs-right">
<li class="nav-item">
<a class="nav-link" href="#">User Name</a>
</li>
</ul>
<form>
<div class="table-cell"> </div>
<div class="table-cell fill-width">
<input class="form-control" name="search" placeholder="Search Here" autocomplete="off" autofocus="autofocus" type="text">
</div>
<div class="table-cell">
<button class="btn btn-outline-success" type="submit">Search</button>
</div>
<div class="table-cell"> </div>
</form>
</nav><em></em> перед <!DOCTYPE html>. После того, как убрал этот тег, всё заработало)<em></em><!DOCTYPE html>
<html>
<head>
<title><%= full_title(yield(:title)) %></title>
<%= stylesheet_link_tag 'application', media: 'all', 'data-turbolinks-track' => true %>
<%= javascript_include_tag 'application', 'data-turbolinks-track' => true, cache: true %>
<%= csrf_meta_tags %>
<%= render 'layouts/shim' %>
<meta name="viewport" content="width=device-width, shrink-to-fit=no, initial-scale=1">
</head>