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I often find that "Search Q&A" is quite useless when I want to find a question or something related to it. But I've also noticed that when I'm about to ask a question, the "Questions that may already have your answer" box has many relevant results.

For example, see this search: failure of uniqueness Cauchy problem. It gives me exactly zero results. Now if you paste the same request into Ask Question title box, you'll get lots of results (including the one I was initially looking for).

So, is it really by design? Does Search Q&A have some different use than what I supposed it does? Wouldn't it be a good idea to at least make the duplicate-finding functionality easier to find since it works better at finding questions by a topic given in free form?

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    $\begingroup$ Good search functionality is something SE is really lacking IMO. I have completely abandoned the "Search Q&A" box for general searches, I now always use the Ask Question button to search. Have you considered posting this on global meta? It may get a better answer there. $\endgroup$
    – PGmath
    Commented Dec 18, 2016 at 5:03
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    $\begingroup$ See also Announcing a third-party search engine for Math StackExchange which often times returns more relevant hits than the built-in search (or the related list for a posted question on the RHS, for that matter). $\endgroup$
    – dxiv
    Commented Dec 18, 2016 at 5:49
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    $\begingroup$ @PGmath I've checked now, and there appears to already exist a question on main Meta, with multiple duplicates. But it seems to have not very useful answers... Should I make yet another duplicate, comparing concrete request given to different engines as is done here? $\endgroup$
    – Ruslan
    Commented Dec 18, 2016 at 15:02
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    $\begingroup$ The Search Q&A tool is a narrow/conservative interpreter of your terms. If you remove "failure of" from the proposed search, one gets 238 results. So my belief is that the Ask Question suggestions are being produced by the same site-specific search, but using subsetting of words in the title. Something similar seems to drive the Related links in the sidebar, where searches make additional use of the [tag] information. $\endgroup$
    – hardmath
    Commented Dec 18, 2016 at 15:27

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