Let's assume we have the following table:

CREATE TABLE test_rum(t text, a tsvector);

CREATE TRIGGER tsvectorupdate
BEFORE UPDATE OR INSERT ON test_rum
FOR EACH ROW EXECUTE PROCEDURE tsvector_update_trigger('a', 'pg_catalog.english', 't');

INSERT INTO test_rum(t) VALUES ('The situation is most beautiful');
INSERT INTO test_rum(t) VALUES ('It is a beautiful');
INSERT INTO test_rum(t) VALUES ('It looks like a beautiful place');

Then we can create a new index:

CREATE INDEX rumidx ON test_rum USING rum (a rum_tsvector_ops);

And we can execute the following queries:

SELECT t, a <=> to_tsquery('english', 'beautiful | place') AS rank
    FROM test_rum
    WHERE a @@ to_tsquery('english', 'beautiful | place')
    ORDER BY a <=> to_tsquery('english', 'beautiful | place');
                t                |   rank
---------------------------------+-----------
 The situation is most beautiful | 0.0303964
 It is a beautiful               | 0.0303964
 It looks like a beautiful place | 0.0607927
(3 rows)

SELECT t, a <=> to_tsquery('english', 'place | situation') AS rank
    FROM test_rum
    WHERE a @@ to_tsquery('english', 'place | situation')
    ORDER BY a <=> to_tsquery('english', 'place | situation');
                t                |   rank
---------------------------------+-----------
 The situation is most beautiful | 0.0303964
 It looks like a beautiful place | 0.0303964
(2 rows)

Let's assume we have the following table:

CREATE TABLE tsts (id int, t tsvector, d timestamp);

\copy tsts from 'rum/data/tsts.data'

CREATE INDEX tsts_idx ON tsts USING rum (t rum_tsvector_addon_ops, d)
    WITH (attach = 'd', to = 't');

Now we can execute the following queries:

EXPLAIN (costs off)
    SELECT id, d, d <=> '2016-05-16 14:21:25' FROM tsts WHERE t @@ 'wr&qh' ORDER BY d <=> '2016-05-16 14:21:25' LIMIT 5;
                                    QUERY PLAN                                     
-----------------------------------------------------------------------------------
 Limit
   ->  Index Scan using tsts_idx on tsts
         Index Cond: (t @@ '''wr'' & ''qh'''::tsquery)
         Order By: (d <=> 'Mon May 16 14:21:25 2016'::timestamp without time zone)
(4 rows)

SELECT id, d, d <=> '2016-05-16 14:21:25' FROM tsts WHERE t @@ 'wr&qh' ORDER BY d <=> '2016-05-16 14:21:25' LIMIT 5;
 id  |                d                |   ?column?    
-----+---------------------------------+---------------
 355 | Mon May 16 14:21:22.326724 2016 |      2.673276
 354 | Mon May 16 13:21:22.326724 2016 |   3602.673276
 371 | Tue May 17 06:21:22.326724 2016 |  57597.326724
 406 | Wed May 18 17:21:22.326724 2016 | 183597.326724
 415 | Thu May 19 02:21:22.326724 2016 | 215997.326724
(5 rows)

Suppose we have the table:

CREATE TABLE query (q tsquery, tag text);

INSERT INTO query VALUES ('supernova & star', 'sn'),
    ('black', 'color'),
    ('big & bang & black & hole', 'bang'),
    ('spiral & galaxy', 'shape'),
    ('black & hole', 'color');

CREATE INDEX query_idx ON query USING rum(q);

We can execute the following fast query:

SELECT * FROM query
    WHERE to_tsvector('black holes never exists before we think about them') @@ q;
        q         |  tag  
------------------+-------
 'black'          | color
 'black' & 'hole' | color
(2 rows)

Let's assume we have the following table:

CREATE TABLE test_array (i int2[]);

INSERT INTO test_array VALUES ('{}'), ('{0}'), ('{1,2,3,4}'), ('{1,2,3}'), ('{1,2}'), ('{1}');

CREATE INDEX idx_array ON test_array USING rum (i rum_anyarray_ops);

Now we can execute the following query using index scan:

SET enable_seqscan TO off;

EXPLAIN (COSTS OFF) SELECT * FROM test_array WHERE i && '{1}' ORDER BY i <=> '{1}' ASC;
                QUERY PLAN
------------------------------------------
 Index Scan using idx_array on test_array
   Index Cond: (i && '{1}'::smallint[])
   Order By: (i <=> '{1}'::smallint[])
(3 rows)

SELECT * FROM test_array WHERE i && '{1}' ORDER BY i <=> '{1}' ASC;
     i
-----------
 {1}
 {1,2}
 {1,2,3}
 {1,2,3,4}
(4 rows)