Eager page freeze criteria clarification

Hi,

While hacking on the pruning and page-level freezing code and am a bit
confused by the test guarding eager freezing  [1]:

    /*
     * Freeze the page when heap_prepare_freeze_tuple indicates that at least
     * one XID/MXID from before FreezeLimit/MultiXactCutoff is present.  Also
     * freeze when pruning generated an FPI, if doing so means that we set the
     * page all-frozen afterwards (might not happen until final heap pass).
     */
    if (pagefrz.freeze_required || tuples_frozen == 0 ||
        (prunestate->all_visible && prunestate->all_frozen &&
         fpi_before != pgWalUsage.wal_fpi))
    {

I'm trying to understand the condition fpi_before !=
pgWalUsage.wal_fpi -- don't eager freeze if pruning emitted an FPI.

Is this test meant to guard against unnecessary freezing or to avoid
freezing when the cost is too high? That is, are we trying to
determine how likely it is that the page has been recently modified
and avoid eager freezing when it would be pointless (because the page
will soon be modified again)? Or are we trying to determine how likely
the freeze record is to emit an FPI and avoid eager freezing when it
isn't worth the cost? Or something else?

The commit message says:

> Also teach VACUUM to trigger page-level freezing whenever it detects
> that heap pruning generated an FPI.  We'll have already written a large
> amount of WAL just to do that much, so it's very likely a good idea to
> get freezing out of the way for the page early.

And I found the thread where it was discussed [2]. Several possible
explanations are mentioned in the thread.

But, the final rationale is still not clear to me. Could we add a
comment above the if condition specifying both:
a) what the test is a proxy for
b) the intended outcome (when do we expect to eager freeze)
And perhaps we could even describe a scenario where this heuristic is effective?

- Melanie

[1] https://github.com/postgres/postgres/blob/master/src/backend/access/heap/vacuumlazy.c#L1802
[2]
https://www.postgresql.org/message-id/flat/CAH2-Wzm_%3DmrWO%2BkUAJbR_gM_6RzpwVA8n8e4nh3dJGHdw_urew%40mail.gmail.com#c5aae6ea65e07de92a24a35445473448