I tried and install InstantSearch in order to achieve better search results. However, your theme has non-compliant HTML, and I cannot use the search and searchbox on the big searchbar in on the front-page. http://kangax.github.io/domlint/
Further more you have a mouseaway function which disables my ability to use their search-suggestion box.
If our search form in the header doesn’t satisfy you, you can replace it with your own form, just edit the file wp-content/themes/woopress/framework/theme-functions.php (from line 1136).
Make changes in your child theme.