Method for widening user search to include more results (show matches of only one word even if multiple are provided, and matching parts of words). Probably not a good idea for high traffic sites, but a blessing for standard ones.

expanded_craft_search.twig

{# Instead of using standard search, like that: #}
{% set query = craft.request.getParam('q') %}
{% set entries = craft.entries.search(query).order('score') %}

{# We can expand it to be more intuitive to the user and give better results: #}
{% set query = craft.request.getParam('q') %}

{# expand query by widening match from `xxx` to `*xxx*`, and `xxx yyy` to `*xxx* *yyy*`, etc #}
{% set expanded_query = query
| replace('/ {2,}/', ' ')
| replace('/(^[^*])/', '*$1')
| replace('/(?<= )([^*])/', '*$1')
| replace('/([^*]$)/', '$1*')
| replace('/([^*])(?= )/', '$1*')
%}

{# switch AND to OR, to have partial match results #}
{% set expanded_query = expanded_query
| replace(' ', ' OR ') %}

{% set entries = craft.entries.search(expanded_query).order('score') %}