I have a problem with a query that is planned wrong. This is my schema:

   create table comments (
     id serial primary key,
     conversation_id integer,
     created_at timestamp
   );
   create index comments_conversation_id_index on comments (conversation_id);
   create index comments_created_at_index on comments (created_at);

The table has 3.5M rows, and 650k unique values for "conversation_id", where 
the histogram goes up to 54000 rows for the most frequent ID, with a long tail. 
There are only 20 values with a frequency of 1000 or higher. The "created_at" 
column has 3.5M distinct values.

Now, I have this query:

   select comments.id from comments where
     conversation_id = 3975979 order by created_at limit 13

This filters about 5000 rows and returns the oldest 13 rows. But the query is 
consistently planned wrong:

   Limit  (cost=0.00..830.53 rows=13 width=12) (actual time=3174.862..3179.525 
rows=13 loops=1)                                                            
     Buffers: shared hit=2400709 read=338923 written=21                         
                                                                           
     ->  Index Scan using comments_created_at_index on comments  
(cost=0.00..359938.52 rows=5634 width=12) (actual time=3174.860..3179.518 
rows=13 loops=1)
           Filter: (conversation_id = 3975979)                                  
                                                                           
           Rows Removed by Filter: 2817751                                      
                                                                           
           Buffers: shared hit=2400709 read=338923 written=21                   
                                                                           
   Total runtime: 3179.553 ms                                                   
                                                                           

It takes anywhere between 3 seconds and several minutes to run, depending on 
how warm the disk cache is. This is the correct plan and index usage:

   Limit  (cost=6214.34..6214.38 rows=13 width=12) (actual time=25.471..25.473 
rows=13 loops=1)                                                                
 
     Buffers: shared hit=197 read=4510                                          
                                                                                
     ->  Sort  (cost=6214.34..6228.02 rows=5471 width=12) (actual 
time=25.469..25.470 rows=13 loops=1)                                            
              
           Sort Key: created_at                                                 
                                                                                
           Sort Method: top-N heapsort  Memory: 25kB                            
                                                                                
           Buffers: shared hit=197 read=4510                                    
                                                                                
           ->  Index Scan using comments_conversation_id_index on comments  
(cost=0.00..6085.76 rows=5471 width=12) (actual time=1.163..23.955 rows=5834 
loops=1)
                 Index Cond: (conversation_id = 3975979)                        
                                                                                
                 Buffers: shared hit=197 read=4510                              
                                                                                
   Total runtime: 25.500 ms                                                     
                                                                                

The problem for Postgres is obviously to estimate how many rows have a given 
"conversation_id" value, but I have confirmed that the value is correctly 
tracked in the histogram.

I'm at a loss how to explain why the planner thinks scanning a huge index that 
covers the entire table will ever beat scanning a small index that has 17% of 
the table's values. Even if the entire database were in RAM, this would hit way 
too much buffers unnecessarily. (I have determined that planner will 
consistently use the bad plan for higher-frequency values, and the good plan 
for lower-frequency values.) It will *always* be better to branch off the 
"comments_conversation_id_index" index.

Another curious thing: If I run ANALYZE repeatedly, the planner will sometimes, 
oddly enough, choose the correct plan. This behaviour actually seems related to 
effective_cache_size; if it's set small (128MB), the planner will sometimes 
favour the good plan, but if large (>= 2GB) it will consistently use the bad 
plan. Not sure if ANALYZE is changing anything or if it's just bad timing.

Things I have tried: I have bumped the statistics target up to 10000, but it 
does not help. I have also tried setting n_distinct for the column manually, 
since Postgres guesses it's 285k instead of 650k, but that does not help.

Our environment: 9.2.2, tweaked memory parameters (work_mem, sort_mem, 
shared_buffers, effective_cache_size), not touched planner/cost parameters. 
Problem also exists on 9.2.3. 




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