# Cardinality Puzzle

One of the difficulties of being a DBA and being required to solve performance problems is that you probably never have enough time to think about how you got to a solution and why the solution works; and if you don’t learn about the process itself , you just don’t get better at it. That’s why I try (at least some of the time) to write articles and books (as I did with CBO Fundamentals) that

1. explain simple details that can be used as background facts
2. walk through the steps of solving a problem

So here’s an example from a question on the ODC database forum asking about the cause and workaround for a bad cardinality estimate that is producing a poorly performing execution plan. It’s actually a type of problem that comes up quite frequently on large data sets and explains why a simple “gather stats” is almost guaranteed to leave you with a few headaches (regardless of whether or not you choose to include histograms as part of the process). I’m not going to offer “the answer” – I’m just going to talk about the inferences we can make from the facts supplied and where we have to go from there.

The DBA has a table holding 80,000,000,000 rows. It is list/hash partitioned with 2 partitions and 1,024 sub-partitions (per partition) but neither of the partitioning key columns appears in the query. The query runs parallel and the optimizer (presumably thanks to the specific settings of various parameters related to parallel execution uses dynamic sampling at level 3).

There is an inline view defined in the query and the DBA has isolated this as a key component of the problem and supplied a query and plan (from “explain plan”) against that view.

```
select * from TAB2 T
WHERE T.DT = to_date(:b1,'MM/DD/YYYY HH24:MI:SS');

------------------------------------------------------------------------------------------------------------------------------------------------------
| Id  | Operation                    | Name                     | Rows  | Bytes | Cost (%CPU)| Time     | Pstart| Pstop |    TQ  |IN-OUT| PQ Distrib |
------------------------------------------------------------------------------------------------------------------------------------------------------
|   0 | SELECT STATEMENT             |                          |   479M|    76G|  1756K (14)| 05:51:14 |       |       |        |      |            |
|   1 |  PX COORDINATOR              |                          |       |       |            |          |       |       |        |      |            |
|   2 |   PX SEND QC (RANDOM)        | :TQ10000                 |   479M|    76G|  1756K (14)| 05:51:14 |       |       |  Q1,00 | P->S | QC (RAND)  |
|   3 |    PX PARTITION HASH ALL     |                          |   479M|    76G|  1756K (14)| 05:51:14 |     1 |  1024 |  Q1,00 | PCWC |            |
|*  4 |     TABLE ACCESS STORAGE FULL| TAB1                     |   479M|    76G|  1756K (14)| 05:51:14 |     1 |  2048 |  Q1,00 | PCWP |            |
------------------------------------------------------------------------------------------------------------------------------------------------------

Predicate Information (identified by operation id):
---------------------------------------------------
4 - storage(COALESCE("TB1"."DFG",'N')='N' AND TRUNC(INTERNAL_FUNCTION("TB1"."DT_TM"))=TO_DATE(:B1,'MM/DD/YYYY
HH24:MI:SS'))
filter(COALESCE("TB1"."DFG",'N')='N' AND TRUNC(INTERNAL_FUNCTION("TB1"."DT_TM"))=TO_DATE(:B1,'MM/DD/YYYY
HH24:MI:SS'))

Note
-----
- dynamic sampling used for this statement (level=3)

```

The DBA’s problem is that if the estimated cardinality of this extract goes over roughly 500M the optimizer chooses a bad plan for the overall query – and on occasion this extract has given an estimate of 5 billion rows. Moreover, the actual number of rows returned by this extract is typically in the order of 40M, so the estimate is a long way off even when it’s “good enough”.

So where do we start looking to work out what’s going wrong? You’ll note, of course, that after text expansion the user’s single predicate has changed, and an extra predicate (previously hidden inside the view) has appeared; instead of just T.DT = to_date(:b1,’MM/DD/YYYY HH24:MI:SS’) we now have (cosmetically adjusted):

```        COALESCE(DFG,'N')='N'
AND     TRUNC(DT_TM)=TO_DATE(:B1,'MM/DD/YYYY HH24:MI:SS')

```

There are two immediately obvious threats here – first that the combination of predicates means Oracle is likely to make a mistake because it will check the individual selectivities and multiply them together to get the combined selectivity, second that the appearance of predicates of the form “function(column) = constant” means that Oracle will guess 1% as the individual selectivities.

Without checking more details we might assume that a possible quick fix (that would require no changes to existing code) would be to create a couple of virtual columns (or extended stats) to represent the two expressions and gather stats on the resulting columns – though it is a restriction of extended stats that you can’t “double up” and create a column group on the two column expressions, so there’s still some scope for a cardinality estimate that is still sufficiently bad even with this approach. We also note that if we can change the coalesce(DFG,’N’) that must have been hidden in the view to nvl(DFG,’N’) then Oracle would be able to “or expand” the nvl() and use a more appropriate selectivity for that part of the predicate.

However, the points I’ve covered so far tend to produce estimates that are too small and often much too small. So maybe the key to the problem is in the Note section that tells us that Oracle has (successfully) used dynamic sampling for this statement. In other words, all the theory of how the optimizer calculates selectivity may be irrelevant – the estimate will be based on the luck of the sample.

So let’s take a look at the (slightly edited) table stats we’ve been given:

```column_name data_type num_distinct low_value      high_value     density   num_null  histogram
DT_TM       DATE           6179571 78740B1E0A383C 7876020B01262B 1.6182E-7 0         NONE
DFG         VARCHAR2             1 4E             4E             1         0         NONE
```

Notice that the DFG (apparently) has the value ‘N’ for every row in the table (low_value = high_value = 0x4E, num_nulls = 0). The date range is 30-Nov-2016 to 11-Feb-2018, with no histogram but 6.18M distinct values for 80 Billion rows. Neither column has a histogram.

A little arithmetic tells us that (on average) there ought to be about 182M (= 80B / 438 days) rows for any one day – and that’s worth thinking about for three separate reasons.

First, an estimate of 479M against an average of 182M isn’t too surprising if it’s based on a fairly small sample, it’s only out by a factor of 2.6. On the other hand, getting an an estimate of 5 billion – which can happen on bad days – is extremely unlikely if the data is uniformly distributed across dates.

Secondly, the DBA supplied us with some data from the recent past with an aggregate query for “trunc(dt_tm)”, with the following results:

```TRUNC(DT_TM)   COUNT(*)
------------ ----------
01-FEB-18    44,254,425
02-FEB-18    46,585,349
03-FEB-18    43,383,099
04-FEB-18    32,748,364
05-FEB-18    37,993,126
06-FEB-18    39,708,994
07-FEB-18    38,696,777
08-FEB-18    41,871,780
09-FEB-18    46,702,852
10-FEB-18    42,744,870
11-FEB-18    34,971,845
12-FEB-18    37,165,983

```

Recent data seems to follow an average of around 40M rows per day, so the estimate of 182M that we can derive from the stored statistics is a long way off: the present is behaving very differently from the past and that’s a relatively common problem with very large data sets – though it’s more usual for rolling averages to increase from the past to the present because the data is often representing the growth of a business over time. Can we create a hypothesis to explain the discrepancy, and could that hypothesis also account for the sample producing some very strange estimates ?

Finally, slightly more subtle and only included for completeness, if this column is supposed to hold date and time to the nearest second – which is what you might expect from an Oracle date type – there are 38 million possible values (438 x 86,400) it could be holding, and that’s more than the actual number of distinct values by a factor of 6. We can also work out that 80 billion rows over 438 days is 2,000 rows per second (on average). Averages are often misleading, of course, many systems have a pattern where a working day shows most of the data created in a 12 – 16 hour window with a couple of hours of more intense activity. For reference, though: average rows per second for the recent data is roughly 40M/86400 = 460; while the average we derive from the stored statistics is 80B / 6M = 13000 rows per second; this unlikely pattern needs a “non-uniform” explanation.

How do these three thoughts help us to understand or, to be more accurate, to make a sensible guess about why the optimizer can use dynamic sampling and get a wildly variable estimate which can be 1 or 2 orders of magnitude wrong. (varying between 479M and 5,000M compared to the recent actual 40M)?

Here’s one simple idea: extrapolate the 40M rows per day over 80B rows: that’s 2,000 days (possibly rather more since businesses tend to grow). What if the dt_tm is the timestamp for the moment the row was loaded into the database, and a couple of years ago (maybe around “30th Nov 2016”) the data was restructured and the existing five years of data was loaded over a very short period of time – let’s say one week. This would leave you with 17B rows of “new” data with a dt_tm spread at 40M rows per day for most of 438 days, and 63B rows of “historic” data packed into 7 days (at 9B rows per day).

I don’t know how Oracle would have randomly selected its sample from an extremely large table with 2,048 physical data segments but it’s totally believable that a small, widely scattered sample could end up with an extremely unrepresentative subset of the data. A completely random sample of the data would produce an estimate of around 500M rows for the predicate; but it would only take a fairly small variation in the sample (taking a few too many “historic” rows) to produce a large enough change in the estimate to change the execution plan, and a rare, but not extreme variation could easily take the estimate up to 5B.

### Next Steps

It would be at this point in a performance assignment that I’d be asking around to find out if my guess about a massive data load operation was correct – if I couldn’t get the answer by talking to people I’d run a query against the whole data set to check the hypothesis, because there’s clearly some sort of skew in the data that’s causing a problem. I’d also run the critical part of the query a couple of times with events 10046/level 4 and 10053 set (but only fetching the first few rows) to find out from the trace file how large a sample Oracle was using, and then run the sampling query a few times to see what the sampled results looked like. Depending on the results I’d either find a way to stop Oracle from sampling for this query or I might create a virtual column (or just extended stats since it’s 11g) on just the trunc(dt_tm), possibly with a histogram in place (maybe coded by hand) if that could isolate the special dates and leave Oracle with a better estimate of the typical date. I might find I had to change the coalesce() to an nvl() as well – or create a virtual  column – to stop the sampling.

Finally, it’s worth noting that in 11g it’s possible to create pending (table preference “PUBLISH” = FALSE) stats for testing purposes; it’s also worth noting that the default histogram on trunc(dt_tm) would be a height-balanced histogram while we could create a frequency histogram in 12c since 12c allows us to specify up to 2,048 buckets.

### Footnote

If you check the ODC thread you’ll see that the OP has marked as correct a suggestion to change:

```    TRUNC (TB1.DT_TM)  = to_date(:b1,'MM/DD/YYYY HH24:MI:SS');
```

to

```    dt_tm >= trunc(to_date(:b1,'MM/DD/YYYY HH24:MI:SS'))
and dt_tm <  trunc(to_date(:b1,'MM/DD/YYYY HH24:MI:SS'))+1
```

Note that that’s “greater than or equal to” at one end and “strictly less than” at the other when using “date + 1”.

This has the effect of giving the optimizer a chance of using the low/high values of the column to produce a better (though perhaps still overlarge) and consistent estimate of the rows in the date range; and it may also stop the optimizer from doing dynamic sampling at level 3 (the “I’m guessing, let’s check” level) though it’s possible that the sampling would be disabled only if the coalesce() were changed to an nvl() as well.

Of course, from the information supplied, this looks like the OP would have to change a view definition and the run-time code to achieve the result. But in an ideal world doing things that avoid confusing the optimizer is usually the sensible strategy provided it doesn’t take an extreme amount of coding and testing.