Partial index plan/cardinality costing

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I have the following tables:
- m(pk bigserial primary key, status text): with a single row
- s(pk bigserial primary key, status text, action_at date, m_fk bigint):
  * 80% of the data has action_at between the current date and 1 year ago
     and status of E or C
  * 20% of the data has action_at between 5 days ago and 25 days into the
     future and status of P, PD, or A

I have two partial indexes:
- s_pk_action_at on s(pk, action_at) where status in ('P', 'PD', 'A')
- s_action_at_pk on s(action_at, pk) where status in ('P', 'PD', 'A')

With the query:
SELECT s.pk FROM s
INNER JOIN m ON m.pk = s.m_fk
WHERE
  s.status IN ('A', 'PD', 'P')
  AND (action_at <= '2018-09-06')
  AND s.status IN ('A', 'P')
  AND m.status = 'A';

I generally expect the index s_action_at_pk to always be preferred over s_pk_action_at. And on stock Postgres it does in fact use that index (with a bitmap index scan).

We like to set random_page_cost = 2 since we use fast SSDs only. With that change Postgres strongly prefers the index s_pk_action_at unless I both disable the other index and turn off bitmap heap scans.

I'm attaching the following plans:
- base_plan.txt: default costs; both indexes available
- base_plan_rpc2.txt: random_page_cost = 2; both indexes available
- inddisabled_plan_rpc2.txt: random_page_cost = 2; only s_action_at_pk available
- inddisabled_bhsoff_plan_rpc2.txt: random_page_cost = 2; enable_bitmapscan = false;  only s_action_at_pk available

A couple of questions:
- How is s_pk_action_at ever efficient to scan? Given that the highest cardinality (primary key) column is first, wouldn't an index scan effectively have to scan the entire index?
- Why does index scan on s_action_at_pk reads over 2x as many blocks as the bitmap heap scan with the same index?
- Would you expect Postgres to generally always prefer using the s_action_at_pk index over the s_pk_action_at index for this query? I realize changing the random page cost is part of what's driving this, but I still can't imagine reading the full s_pk_action_at index (assuming that's what it is doing) could ever be more valuable.

As a side note, the planner is very bad at understanding a query that happens (I realize you wouldn't write this by hand, but ORMs) when you have a where clause like:
    s.status IN ('A', 'PD', 'P') AND s.status IN ('A', 'P')
the row estimates are significantly different from a where clause with only:
    s.status IN ('A', 'P')
even though semantically those are identical.


                                                             QUERY PLAN                                                             
------------------------------------------------------------------------------------------------------------------------------------
 Nested Loop  (cost=0.42..8795.84 rows=11004 width=8) (actual time=0.020..12.338 rows=8919 loops=1)
   Join Filter: (s.m_fk = m.pk)
   Buffers: shared hit=8234
   ->  Seq Scan on m  (cost=0.00..1.01 rows=1 width=8) (actual time=0.004..0.005 rows=1 loops=1)
         Filter: (status = 'A'::text)
         Buffers: shared hit=1
   ->  Index Scan using s_action_at_pk on s  (cost=0.42..8657.28 rows=11004 width=16) (actual time=0.014..11.008 rows=8919 loops=1)
         Index Cond: (action_at <= '2018-09-06'::date)
         Filter: (status = ANY ('{A,P}'::text[]))
         Rows Removed by Filter: 4483
         Buffers: shared hit=8233
 Planning Time: 0.502 ms
 Execution Time: 12.793 ms
(13 rows)
                                                               QUERY PLAN                                                               
----------------------------------------------------------------------------------------------------------------------------------------
 Nested Loop  (cost=1900.77..6768.34 rows=11004 width=8) (actual time=1.345..11.812 rows=8919 loops=1)
   Join Filter: (s.m_fk = m.pk)
   Buffers: shared hit=3184
   ->  Seq Scan on m  (cost=0.00..1.01 rows=1 width=8) (actual time=0.005..0.006 rows=1 loops=1)
         Filter: (status = 'A'::text)
         Buffers: shared hit=1
   ->  Bitmap Heap Scan on s  (cost=1900.77..6629.78 rows=11004 width=16) (actual time=1.337..10.515 rows=8919 loops=1)
         Recheck Cond: ((action_at <= '2018-09-06'::date) AND (status = ANY ('{P,PD,A}'::text[])))
         Filter: (status = ANY ('{A,P}'::text[]))
         Rows Removed by Filter: 4483
         Heap Blocks: exact=3129
         Buffers: shared hit=3183
         ->  Bitmap Index Scan on s_action_at_pk  (cost=0.00..1898.02 rows=82347 width=0) (actual time=0.995..0.995 rows=13402 loops=1)
               Index Cond: (action_at <= '2018-09-06'::date)
               Buffers: shared hit=54
 Planning Time: 0.719 ms
 Execution Time: 12.288 ms
(17 rows)
                                                             QUERY PLAN                                                             
------------------------------------------------------------------------------------------------------------------------------------
 Nested Loop  (cost=0.42..5768.94 rows=11004 width=8) (actual time=0.062..14.308 rows=8919 loops=1)
   Join Filter: (s.m_fk = m.pk)
   Buffers: shared hit=3130 read=386
   ->  Seq Scan on m  (cost=0.00..1.01 rows=1 width=8) (actual time=0.004..0.006 rows=1 loops=1)
         Filter: (status = 'A'::text)
         Buffers: shared hit=1
   ->  Index Scan using s_pk_action_at on s  (cost=0.42..5630.38 rows=11004 width=16) (actual time=0.056..13.012 rows=8919 loops=1)
         Index Cond: (action_at <= '2018-09-06'::date)
         Filter: (status = ANY ('{A,P}'::text[]))
         Rows Removed by Filter: 4483
         Buffers: shared hit=3129 read=386
 Planning Time: 0.704 ms
 Execution Time: 14.843 ms
(13 rows)
                                                               QUERY PLAN                                                               
----------------------------------------------------------------------------------------------------------------------------------------
 Nested Loop  (cost=1260.77..6128.34 rows=11004 width=8) (actual time=1.375..11.957 rows=8919 loops=1)
   Join Filter: (s.m_fk = m.pk)
   Buffers: shared hit=3184
   ->  Seq Scan on m  (cost=0.00..1.01 rows=1 width=8) (actual time=0.003..0.004 rows=1 loops=1)
         Filter: (status = 'A'::text)
         Buffers: shared hit=1
   ->  Bitmap Heap Scan on s  (cost=1260.77..5989.78 rows=11004 width=16) (actual time=1.369..10.549 rows=8919 loops=1)
         Recheck Cond: ((action_at <= '2018-09-06'::date) AND (status = ANY ('{P,PD,A}'::text[])))
         Filter: (status = ANY ('{A,P}'::text[]))
         Rows Removed by Filter: 4483
         Heap Blocks: exact=3129
         Buffers: shared hit=3183
         ->  Bitmap Index Scan on s_action_at_pk  (cost=0.00..1258.02 rows=82347 width=0) (actual time=1.026..1.026 rows=13402 loops=1)
               Index Cond: (action_at <= '2018-09-06'::date)
               Buffers: shared hit=54
 Planning Time: 0.500 ms
 Execution Time: 12.437 ms
(17 rows)

Attachment: query.sql
Description: application/sql

Attachment: setup.sql
Description: application/sql


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