Add estimated hit ratio to Memoize in EXPLAIN to explain cost adjustment

Hi,

I was debugging a planner problem on Postgres 14.4 the other day - and the
involved "bad" plan was including Memoize - though I don't necessarily
think that Memoize is to blame (and this isn't any of the problems recently
fixed in Memoize costing).

However, what I noticed whilst trying different ways to fix the plan, is
that the Memoize output was a bit hard to reason about - especially since
the plan involving Memoize was expensive to run, and so I was mostly
running EXPLAIN without ANALYZE to look at the costing.

Here is an example of the output I was looking at:

-> Nested Loop (cost=1.00..971672.56 rows=119623 width=0)
-> Index Only Scan using table1_idx on table1
(cost=0.43..372676.50 rows=23553966 width=8)
-> Memoize (cost=0.57..0.61 rows=1 width=8)
Cache Key: table1.table2_id
Cache Mode: logical
-> Index Scan using table2_idx on table2
(cost=0.56..0.60 rows=1 width=8)
Index Cond: (id = table1.table2_id)

The other plan I was comparing with (that I wanted the planner to choose
instead), had a total cost of 1,451,807.35 -- and so I was trying to figure
out why the Nested Loop was costed as 971,672.56.

Simple math makes me expect the Nested Loop should roughly have a total
cost of14,740,595.76 here (372,676.50 + 23,553,966 * 0.61), ignoring a lot
of the smaller costs. Thus, in this example, it appears Memoize made the
plan cost significantly cheaper (roughly 6% of the regular cost).

Essentially this comes down to the "cost reduction" performed by Memoize
only being implicitly visible in the Nested Loop's total cost - and with
nothing useful on the Memoize node itself - since the rescan costs are not
shown.

I think explicitly adding the estimated cache hit ratio for Memoize nodes
might make this easier to reason about, like this:

-> Memoize (cost=0.57..0.61 rows=1 width=8)
Cache Key: table1.table2_id
Cache Mode: logical
Cache Hit Ratio Estimated: 0.94

Alternatively (or in addition) we could consider showing the "ndistinct"
value that is calculated in cost_memoize_rescan - since that's the most
significant contributor to the cache hit ratio (and you can influence that
directly by improving the ndistinct statistics).

See attached a patch that implements showing the cache hit ratio as a
discussion starter.

I'll park this in the July commitfest for now.

Thanks,
Lukas

--
Lukas Fittl