# Re: [HACKERS] multivariate statistics v14

```>> I am now looking into the create statistics doc to see if the example
>> appearing in it is working. I will get back if I find any.```
```
I have the ref doc: CREATE STATISTICS

There are nice examples how the multivariate statistics gives better
row number estimation. So I gave them a try.

"Create table t1 with two functionally dependent columns,
i.e. knowledge of a value in the first column is sufficient for
determining the value in the other column" The example creates table
"t1", then populates it using generate_series. After CREATE
STATISTICS, ANALYZE and EXPLAIN. I expected the EXPLAIN demonstrates
how result rows estimation is enhanced by using the multivariate
statistics.

Here is the EXPLAIN output using the multivariate statistics:

EXPLAIN ANALYZE SELECT * FROM t1 WHERE (a = 1) AND (b = 1);
QUERY PLAN

---------------------------------------------------------------------------------------------------
Seq Scan on t1  (cost=0.00..19425.00 rows=98 width=8) (actual
time=76.876..76.876 rows=0 loops=1)
Filter: ((a = 1) AND (b = 1))
Rows Removed by Filter: 1000000
Planning time: 0.146 ms
Execution time: 76.896 ms
(5 rows)

Here is the EXPLAIN output without the multivariate statistics:

EXPLAIN ANALYZE SELECT * FROM t1 WHERE (a = 1) AND (b = 1);
QUERY PLAN

--------------------------------------------------------------------------------------------------
Seq Scan on t1  (cost=0.00..19425.00 rows=1 width=8) (actual
time=78.867..78.867 rows=0 loops=1)
Filter: ((a = 1) AND (b = 1))
Rows Removed by Filter: 1000000
Planning time: 0.102 ms
Execution time: 78.885 ms
(5 rows)

It seems the row numbers estimation (98) using the multivariate
statistics is actually *worse* than the one (1) not using the
statistics because the actual row number is 0.

Next example (using table "t2") is much better than the case using t1.

Here is the EXPLAIN output using the multivariate statistics:

EXPLAIN ANALYZE SELECT * FROM t2 WHERE (a = 1) AND (b = 1);
QUERY PLAN

--------------------------------------------------------------------------------------------------------
Seq Scan on t2  (cost=0.00..19425.00 rows=9633 width=8) (actual
time=0.012..75.350 rows=10000 loops=1)
Filter: ((a = 1) AND (b = 1))
Rows Removed by Filter: 990000
Planning time: 0.107 ms
Execution time: 75.680 ms
(5 rows)

Here is the EXPLAIN output without the multivariate statistics:

EXPLAIN ANALYZE SELECT * FROM t2 WHERE (a = 1) AND (b = 1);
QUERY PLAN

------------------------------------------------------------------------------------------------------
Seq Scan on t2  (cost=0.00..19425.00 rows=91 width=8) (actual
time=0.008..76.614 rows=10000 loops=1)
Filter: ((a = 1) AND (b = 1))
Rows Removed by Filter: 990000
Planning time: 0.067 ms
Execution time: 76.935 ms
(5 rows)

This time it seems the row numbers estimation (9633) using the
multivariate statistics is much better than the one (91) not using the
statistics because the actual row number is 10000.

The last example (using table "t3") seems no effect by multivariate statistics.

Here is the EXPLAIN output using the multivariate statistics:

EXPLAIN ANALYZE SELECT * FROM t3 WHERE (a < 500) AND (b > 500);
QUERY PLAN

-----------------------------------------------------------------------------------------------------------
Seq Scan on t3  (cost=0.00..20407.65 rows=111123 width=16) (actual
time=0.154..132.509 rows=6002 loops=1)
Filter: ((a < '500'::double precision) AND (b > '500'::double precision))
Rows Removed by Filter: 993998
Planning time: 0.080 ms
Execution time: 132.735 ms
(5 rows)

EXPLAIN ANALYZE SELECT * FROM t3 WHERE (a < 400) AND (b > 600);
QUERY PLAN

----------------------------------------------------------------------------------------------------------
Seq Scan on t3  (cost=0.00..20407.65 rows=111123 width=16) (actual
time=110.518..110.518 rows=0 loops=1)
Filter: ((a < '400'::double precision) AND (b > '600'::double precision))
Rows Removed by Filter: 1000000
Planning time: 0.052 ms
Execution time: 110.531 ms
(5 rows)

Here is the EXPLAIN output without the multivariate statistics:

EXPLAIN ANALYZE SELECT * FROM t3 WHERE (a < 500) AND (b > 500);
QUERY PLAN

-----------------------------------------------------------------------------------------------------------
Seq Scan on t3  (cost=0.00..20407.65 rows=111123 width=16) (actual
time=0.149..129.718 rows=5999 loops=1)
Filter: ((a < '500'::double precision) AND (b > '500'::double precision))
Rows Removed by Filter: 994001
Planning time: 0.058 ms
Execution time: 129.893 ms
(5 rows)

EXPLAIN ANALYZE SELECT * FROM t3 WHERE (a < 400) AND (b > 600);
QUERY PLAN

----------------------------------------------------------------------------------------------------------
Seq Scan on t3  (cost=0.00..20407.65 rows=111123 width=16) (actual
time=108.015..108.015 rows=0 loops=1)
Filter: ((a < '400'::double precision) AND (b > '600'::double precision))
Rows Removed by Filter: 1000000
Planning time: 0.037 ms
Execution time: 108.027 ms
(5 rows)

This time it seems the row numbers estimation (111123) using the
multivariate statistics is same as same as the one (111123) not
using the statistics because the actual row number is 5999 or 0.

In summary, the only case which shows the effect of the multivariate
statistics is the "t2" case. So I don't see why other examples are
shown in the manual. Am I missing something?

Best regards,
--
Tatsuo Ishii
SRA OSS, Inc. Japan
English: http://www.sraoss.co.jp/index_en.php
Japanese:http://www.sraoss.co.jp

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