using the Crd2Cnt transformation which returns a model $M'$ for estimating containment rates. The obtained model $M'$ functions as follows. Given input queries $Q1$ and $Q2$, whose containment rate $Q1 \subset_{\%} Q2$ needs to be estimated:

-   Calculate the cardinality of query $Q1{\mbox{$\cap$}}Q2$ using $M$.

-   Calculate the cardinality of query $Q1$ using $M$.

-   Then, the containment rate estimate is: $$Q1 \subset_{\%} Q2 = \frac{|Q1{\mbox{$\cap$}}Q2|}{|Q1|}$$

Here, $Q1{\mbox{$\cap$}}Q2$ is the intersection query of $Q1$ and $Q2$ whose SELECT and FROM clauses are identical to $Q1$’s (or $Q2$’s) clauses, and whose WHERE clause is $Q1$’s AND $Q2$’s WHERE clauses. Note that, by definition, if $|Q1|=0$ then $Q1 \subset_{\%} Q2=0$.

Given model $M$, we denote the obtained model $M'$, via the Crd2Cnt transformation, as Crd2Cnt($M$).

We compared the CRN model predictions to those based on the other examined cardinality estimation models, using the Crd2Cnt transformation. We examined the PostgreSQL version 11 cardinality estimation component [@postgreSQL], a simple and commonly used method for cardinality estimation. In addition, we examined the MSCN model [@LearnedCrd]. MSCN was shown to be superior to the best methods for estimating cardinalities such as Random Sampling (RS) [@RS1; @RS2] and the state-of-the-art Index-Based Join Sampling (IBJS) [@IBJS].

### Comparing 