Best way to use PostgreSQL full text search ranking

Following on from this answer I want to know what the best way to use PostgreSQL's built-in full text search is if I want to sort by rank, and limit to only matching queries.

Let's assume a very simple table.

CREATE TABLE pictures (
  id SERIAL PRIMARY KEY,
  title varchar(300),
  ...
)

or whatever. Now I want to search the title field. First I create an index:

CREATE INDEX pictures_title ON pictures 
  USING gin(to_tsvector('english', title));

Now I want to search for 'small dog'. This works:

SELECT pictures.id, 
       ts_rank_cd(
         to_tsvector('english', pictures.title), 'small dog'
       ) AS score
FROM pictures
ORDER BY score DESC

But what I really want is this:

SELECT pictures.id, 
       ts_rank_cd(
         to_tsvector('english', pictures.title), to_tsquery('small dog')
       ) AS score
FROM pictures 
WHERE to_tsvector('english', pictures.title) @@ to_tsquery('small dog')
ORDER BY score DESC

Or alternatively this (which doesn't work - can't use score in the WHERE clause):

SELECT pictures.id, 
       ts_rank_cd(
         to_tsvector('english', pictures.title), to_tsquery('small dog')
       ) AS score
FROM pictures WHERE score > 0
ORDER BY score DESC

What's the best way to do this? My questions are many-fold:

If I use the version with repeated to_tsvector(...) will it call that twice, or is it smart enough to cache the results somehow?
Is there a way to do it without repeating the to_ts... function calls?
Is there a way to use score in the WHERE clause at all?
If there is, would it be better to filter by score > 0 or use the @@ thing?

Solution

The use of the @@ operator will utilize the full text GIN index, while the test for score > 0 would not.

I created a table as in the Question, but added a column named title_tsv:

CREATE TABLE test_pictures (
  id        BIGSERIAL,
  title     text,
  title_tsv tsvector
);

CREATE INDEX ix_pictures_title_tsv ON test_pictures 
    USING gin(title_tsv);

I populated the table with some test data:

INSERT INTO test_pictures(title, title_tsv)
SELECT T.data, to_tsvector(T.data) 
FROM   some_table T;

Then I ran the previously accepted answer with explain analyze:

EXPLAIN ANALYZE 
SELECT  score, id, title
FROM (
    SELECT ts_rank_cd(P.title_tsv, to_tsquery('address & shipping')) AS score
        ,P.id        
        ,P.title
    FROM test_pictures as P
) S
WHERE score > 0
ORDER BY score DESC;

And got the following. Note the execution time of 5,015 ms

QUERY PLAN                                                                                                                                    |
----------------------------------------------------------------------------------------------------------------------------------------------|
Gather Merge  (cost=274895.48..323298.03 rows=414850 width=60) (actual time=5010.844..5011.330 rows=1477 loops=1)                             |
  Workers Planned: 2                                                                                                                          |
  Workers Launched: 2                                                                                                                         |
  ->  Sort  (cost=273895.46..274414.02 rows=207425 width=60) (actual time=4994.539..4994.555 rows=492 loops=3)                                |
        Sort Key: (ts_rank_cd(p.title_tsv, to_tsquery('address & shipping'::text))) DESC                                                      |
        Sort Method: quicksort  Memory: 131kB                                                                                                 |
        ->  Parallel Seq Scan on test_pictures p  (cost=0.00..247776.02 rows=207425 width=60) (actual time=17.672..4993.997 rows=492 loops=3) |
              Filter: (ts_rank_cd(title_tsv, to_tsquery('address & shipping'::text)) > '0'::double precision)                                 |
              Rows Removed by Filter: 497296                                                                                                  |
Planning time: 0.159 ms                                                                                                                       |
Execution time: 5015.664 ms                                                                                                                   |

Now compare that with the @@ operator:

EXPLAIN ANALYZE
SELECT ts_rank_cd(to_tsvector(P.title), to_tsquery('address & shipping')) AS score
    ,P.id
    ,P.title
FROM    test_pictures as P
WHERE P.title_tsv @@ to_tsquery('address & shipping')
ORDER BY score DESC;

And the results coming in with an execution time of about 29 ms:

QUERY PLAN                                                                                                                                       |
-------------------------------------------------------------------------------------------------------------------------------------------------|
Gather Merge  (cost=13884.42..14288.35 rows=3462 width=60) (actual time=26.472..26.942 rows=1477 loops=1)                                        |
  Workers Planned: 2                                                                                                                             |
  Workers Launched: 2                                                                                                                            |
  ->  Sort  (cost=12884.40..12888.73 rows=1731 width=60) (actual time=17.507..17.524 rows=492 loops=3)                                           |
        Sort Key: (ts_rank_cd(to_tsvector(title), to_tsquery('address & shipping'::text))) DESC                                                  |
        Sort Method: quicksort  Memory: 171kB                                                                                                    |
        ->  Parallel Bitmap Heap Scan on test_pictures p  (cost=72.45..12791.29 rows=1731 width=60) (actual time=1.781..17.268 rows=492 loops=3) |
              Recheck Cond: (title_tsv @@ to_tsquery('address & shipping'::text))                                                                |
              Heap Blocks: exact=625                                                                                                             |
              ->  Bitmap Index Scan on ix_pictures_title_tsv  (cost=0.00..71.41 rows=4155 width=0) (actual time=3.765..3.765 rows=1477 loops=1)  |
                    Index Cond: (title_tsv @@ to_tsquery('address & shipping'::text))                                                            |
Planning time: 0.214 ms                                                                                                                          |
Execution time: 28.995 ms                                                                                                                        |

As you can see in the execution plan, the index ix_pictures_title_tsv was used in the second query, but not in the first one, making the query with the @@ operator a whopping 172 times faster!