nginx : rewrite rule to remove /index.html from the $request_uri

The following config allowed me to redirect /index.html to / and /subdir/index.html to /subdir/:

# Strip "index.html" (for canonicalization)
if ( $request_uri ~ "/index.html" ) {
    rewrite ^(.*)/ $1/ permanent;
}

I use the following rewrite in the top level server clause:

rewrite ^(.*)/index\.html$ $1 permanent;

Using this alone works for most URLs, like http://example.com/bar/index.html, but it breaks http://example.com/index.html. To resolve this, I have the following additional rule:

location = /index.html {
  rewrite  ^ / permanent;
  try_files /index.html =404;
}

The =404 part returns a 404 error when the file is not found.

I have no idea why the first rewrite alone isn't sufficient.