Not only by phrase! Not only on website! Quick product search, too!
I found, probably part, of the answer. Operators

%

and

_

works (postgresql like, ilike oerators).

Search on forum today eg. by:

• button%print = 140 results
• button %print = 111 results
• button % print = 87 results
• print%button = 175 results
• _mail_ = 1590 results

@zbik,

I've also asked a similar question on a few other threads in this forum. I'd recommend watching this project:

https://github.com/akretion/solerp

specifically the (now closed) issue here:

https://github.com/akretion/solerp/issues/3

There's a forum post here for a fork for an FTS framework in Odoo [8.0] that is discussed here:
https://www.odoo.com/forum/help-1/question/fulltext-search-fts-migrate-to-odoo-8-0-full-text-search-support-in-forum-55060

This is the fork:
https://github.com/straga/odoo-addon_fts

My forum post discussiong improved search in Odoo is here:

https://www.odoo.com/forum/help-1/question/enhanced-improved-front-end-e-commerce-cms-search-module-57233

I think either SolR, or Sphinx (search) implementations would both be workable solutions. Sphinx may be slightly easier to setup, but both have their pros and cons.

I have already spoken to a SaaS Sphinx search provider called searchanise in regards to plugging into their API for use with Odoo due to the comparitevely lower initial setup cost (ie. not starting to build it from scratch), however a completely open-source, standalone solution as it would obviously be more desireable for the majority and in the long run.

If there was enough interest I would consider putting together a funding campaign to get this project off the ground, however it would require some interest from larger parties in order to get the funding required to get the project off the ground.

In the meantime I think the FTS addon I linked to above may hold the key to putting all of these modules together in one global search for the frontend (CMS, products, forum posts, news, etc.) and eventually one global search bar for the backend (although this is a much larger undertaking and may be better handled by Odoo SA in Odoo [9.0] core).