Postgresql partitioned table timestamptz constraint problem
I cannot fully respond as to why date_trunc('day', CURRENT_TIMESTAMP) is not equivalent to a constant... even if both CURRENT_TIMESTAMP and date_trunc are defined as IMMUTABLE. 

But I think we can make an experimental educated guess: Apparently, the PostgreSQL planner does not evaluate functions. As such, it doesn't have any good way to know which partitions to check, and makes a plan that checks them all. 



Experimental check

We create a base (parent) table:

 -- Base table
 CREATE TABLE reports
 (
     rpt_datetime timestamp without time zone DEFAULT now() PRIMARY KEY,
     rpt_unique_clicks integer NOT NULL DEFAULT 1,
     something_else text
 ) ;


We create an auto-partition insert trigger:

 -- Auto-partition using trigger
 -- Adapted from http://blog.l1x.me/post/2016/02/16/creating-partitions-automatically-in-postgresql.html
 CREATE OR REPLACE FUNCTION create_partition_and_insert ()
 RETURNS TRIGGER AS 
 $$
 DECLARE
     _partition_date text ;
     _partition_date_p1 text ;
     _partition text ;
 BEGIN
     _partition_date := to_char(new.rpt_datetime, 'YYYYMMDD');
     _partition := 'reports_' || _partition_date ;

     -- Check if table exists... 
     -- (oversimplistic: doesn't take schemas into account... doesn't check for possible race conditions)
     if not exists (SELECT relname FROM pg_class WHERE relname=_partition) THEN
        _partition_date_p1 := to_char(new.rpt_datetime + interval '1 day', 'YYYYMMDD');

        RAISE NOTICE 'Creating %', _partition ;

        EXECUTE 'CREATE TABLE ' || _partition || 
              ' (CHECK (rpt_datetime &gt;= timestamp ''' || _partition_date || ''' AND rpt_datetime &lt; timestamp ''' || _partition_date_p1 || '''))' ||
              ' INHERITS (reports)' ;
     end if ;

     EXECUTE 'INSERT INTO ' || _partition || ' SELECT(reports ' || quote_literal(NEW) || ').* ;' ;

     -- We won't insert anything on parent table
     RETURN NULL ;
 END 
 $$
 LANGUAGE plpgsql VOLATILE
 COST 1000;

 -- Attach trigger to parent table
 CREATE TRIGGER reports_insert_trigger
 BEFORE INSERT ON reports
 FOR EACH ROW EXECUTE PROCEDURE create_partition_and_insert();


Fill the (partitioned) table with some data; and check the partitions the trigger made:

 INSERT INTO 
     reports (rpt_datetime, rpt_unique_clicks, something_else)
 SELECT
     d, 1, 'Hello'
 FROM
     generate_series(timestamp '20170416' - interval '7 days', timestamp '20170416', interval '10 minutes') x(d) ;

 -- Check how many partitions we made
 SELECT 
     table_name 
 FROM 
      information_schema.tables 
 WHERE 
     table_name like 'reports_%' 
 ORDER BY 
     table_name;



 | table_name       |
 | :--------------- |
 | reports_20170409 |
 | reports_20170410 |
 | reports_20170411 |
 | reports_20170412 |
 | reports_20170413 |
 | reports_20170414 |
 | reports_20170415 |
 | reports_20170416 |
 

At this point, we check two different queries. The first one does use a constant compared to rpt_datetime:

 EXPLAIN (ANALYZE) 
 SELECT 
     SUM(rpt_unique_clicks) 
 FROM 
     reports 
 WHERE 
     rpt_datetime &gt;= timestamp '20170416' ; 


Using a constant timestamp, only 'reports' and the appropriate partition are checked:


 | QUERY PLAN                                                                                                              |
 | :---------------------------------------------------------------------------------------------------------------------- |
 | Aggregate  (cost=25.07..25.08 rows=1 width=8) (actual time=0.015..0.015 rows=1 loops=1)                                 |
 |   -&gt;  Append  (cost=0.00..24.12 rows=378 width=4) (actual time=0.009..0.010 rows=1 loops=1)                             |
 |         -&gt;  Seq Scan on reports  (cost=0.00..0.00 rows=1 width=4) (actual time=0.003..0.003 rows=0 loops=1)             |
 |               Filter: (rpt_datetime &gt;= '2017-04-16 00:00:00'::timestamp without time zone)                              |
 |         -&gt;  Seq Scan on reports_20170416  (cost=0.00..24.12 rows=377 width=4) (actual time=0.006..0.007 rows=1 loops=1) |
 |               Filter: (rpt_datetime &gt;= '2017-04-16 00:00:00'::timestamp without time zone)                              |
 | Planning time: 0.713 ms                                                                                                 |
 | Execution time: 0.040 ms                                                                                                |
 

If we use the equivalent SELECT using a function-call (even if the result of this function call is a constant), the plan is completely different:

 EXPLAIN (ANALYZE) 
 SELECT 
     SUM(rpt_unique_clicks) 
 FROM 
     reports 
 WHERE 
     rpt_datetime &gt;= date_trunc('day', now()) ;  



 | QUERY PLAN                                                                                                              |
 | :---------------------------------------------------------------------------------------------------------------------- |
 | Aggregate  (cost=245.74..245.75 rows=1 width=8) (actual time=0.842..0.843 rows=1 loops=1)                               |
 |   -&gt;  Append  (cost=0.00..238.20 rows=3017 width=4) (actual time=0.837..0.838 rows=1 loops=1)                           |
 |         -&gt;  Seq Scan on reports  (cost=0.00..0.00 rows=1 width=4) (actual time=0.003..0.003 rows=0 loops=1)             |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 |         -&gt;  Seq Scan on reports_20170409  (cost=0.00..29.78 rows=377 width=4) (actual time=0.214..0.214 rows=0 loops=1) |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 |               Rows Removed by Filter: 144                                                                               |
 |         -&gt;  Seq Scan on reports_20170410  (cost=0.00..29.78 rows=377 width=4) (actual time=0.097..0.097 rows=0 loops=1) |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 |               Rows Removed by Filter: 144                                                                               |
 |         -&gt;  Seq Scan on reports_20170411  (cost=0.00..29.78 rows=377 width=4) (actual time=0.095..0.095 rows=0 loops=1) |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 |               Rows Removed by Filter: 144                                                                               |
 |         -&gt;  Seq Scan on reports_20170412  (cost=0.00..29.78 rows=377 width=4) (actual time=0.096..0.096 rows=0 loops=1) |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 |               Rows Removed by Filter: 144                                                                               |
 |         -&gt;  Seq Scan on reports_20170413  (cost=0.00..29.78 rows=377 width=4) (actual time=0.131..0.131 rows=0 loops=1) |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 |               Rows Removed by Filter: 144                                                                               |
 |         -&gt;  Seq Scan on reports_20170414  (cost=0.00..29.78 rows=377 width=4) (actual time=0.098..0.098 rows=0 loops=1) |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 |               Rows Removed by Filter: 144                                                                               |
 |         -&gt;  Seq Scan on reports_20170415  (cost=0.00..29.78 rows=377 width=4) (actual time=0.095..0.095 rows=0 loops=1) |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 |               Rows Removed by Filter: 144                                                                               |
 |         -&gt;  Seq Scan on reports_20170416  (cost=0.00..29.78 rows=377 width=4) (actual time=0.004..0.005 rows=1 loops=1) |
 |               Filter: (rpt_datetime &gt;= date_trunc('day'::text, now()))                                                  |
 | Planning time: 0.298 ms                                                                                                 |
 | Execution time: 0.892 ms                                                                                                |
 

dbfiddle here