Hi!
The search speed is determined by many factors, that’s why I put together a documentation chapter for speed improvement tips for mainly shared hosting environments: https://goo.gl/Rn6lG6
There are 7 different suggestions, ordered by performance impact. I strongly recommend following the first 4 at least, it should result in a significant speed boost.
You can further track the plugin performance with the built in performance tracker, which tracks the clear plugin execution time: https://goo.gl/RAVB3S
It’s a great tool to help you investigate speed related issues related to possible 3rd party plugins or themes.