SQL cross join query slower than expected, refactoring ideas needed - oracle

Question

This query works but takes 5000 miliseconds.
SELECT
SUM(case
when ((TRUNC(OPEN_DATE) <= thedate and TRUNC(END_DATE) > thedate) or(TRUNC(OPEN_DATE) <= thedate and END_DATE Is Null)) then 1
else 0
end) as Open
From (
select *
FROM PROJECT
WHERE
PROGRAM_NAME = :program
AND ACTION_FOR_ORG = :orgName
)
cross join (
select add_months(last_day(SYSDATE), level-7) as thedate
from dual
connect by level <= 12
)
GROUP BY thedate
ORDER BY thedate
If I copy the subquery to its own table
create table test_project as
select * FROM PROJECT WHERE PROGRAM_NAME = :program
AND ACTION_FOR_ORG = :orgName
then do the above query but the subquery is on the copied table as:
From ( select * FROM test_project WHERE PROGRAM_NAME = :program
AND ACTION_FOR_ORG = :orgName )
the query takes 10 milliseconds
The query produces a count of how many projects were open in that month over the past 5 and future months (count of open projects for furture months will just equal todays months totals) based on comparing OPEN_DATE to END_DATE
Is there a way to rewrite the original query for optimal performance?
EDIT
OK, I created a second table which is a full copy of the project table (well view) that I was allowed access to. The table copy took about 5 seconds. Using the full set of data and either my sql query or from Egor below, the query is super fast. Something is up with the view. Trying to spit out explain plan using the View in the subquery I get insufficient privileges. Here is the explain plan using a full copy of the view
Plan hash value: 3695211866
------------------------------------------------------------------------------------------------
| Id | Operation | Name | Rows | Bytes | Cost (%CPU)| Time |
------------------------------------------------------------------------------------------------
| 0 | SELECT STATEMENT | | 637 | 1277K| 163 (2)| 00:00:02 |
| 1 | SORT ORDER BY | | 637 | 1277K| 163 (2)| 00:00:02 |
| 2 | HASH GROUP BY | | 637 | 1277K| 163 (2)| 00:00:02 |
| 3 | MERGE JOIN CARTESIAN | | 637 | 1277K| 161 (0)| 00:00:02 |
| 4 | VIEW | | 1 | 6 | 2 (0)| 00:00:01 |
|* 5 | CONNECT BY WITHOUT FILTERING| | | | | |
| 6 | FAST DUAL | | 1 | | 2 (0)| 00:00:01 |
| 7 | BUFFER SORT | | 637 | 1273K| 163 (2)| 00:00:02 |
|* 8 | TABLE ACCESS FULL | COMMIT_TEST | 637 | 1273K| 159 (0)| 00:00:02 |
Predicate Information (identified by operation id):
5 - filter(LEVEL<=12)
8 - filter("PROGRAM_NAME"='program_name' AND "ACTION_FOR_ORG"='action_for_org')
Note
- dynamic sampling used for this statement (level=2)
Explain Plan using live table

Answer 1

with
PRJ as (
select /*+ NO_UNNEST */
trunc(OPEN_DATE) as OPEN_DATE,
nvl(trunc(END_DATE), sysdate + 1000) as END_DATE
from
PROJECT
where
PROGRAM_NAME = :program
and ACTION_FOR_ORG = :orgName
),
DATES as (
select
add_months(trunc(last_day(SYSDATE)), level-7) as thedate
from dual
connect by level <= 12
)
SELECT
thedate,
sum(case when thedate between open_date and end_date then 1 end) as Open
FROM
DATES, PRJ
GROUP BY thedate
ORDER BY 1