Re: Immutable function WAY slower than Stable function?

I'm definitely not understanding why or how auto-explain would help here.  (Also, don't overlook the fact that both si_stable and si_imm have the exact same definition (except for stable v. immutable), and are calling the same function (staff_inspector_stable)).  I can load up the auto_explain stuff if it really will help, but in the meantime what I did was pull the query out of staff_inspector_stable, and inserted into the "SELECT client_id,staff_inspector( ... ) FROM tbl_residence_own" query, replacing the "client" (parameter 1) with the client_id from the tbl_residence_own, and replacing "asof" (parameter 2) with target_date(), which seems like it should closely mimic the original query.  

I ended up with the query below, and have attached the explain output to this email.  The actual timing is:

 Planning time: 2.737 msExecution time: 821.034 ms

Which is somewhat better than the function versions, though it seems unsurprisingly and not dramatically so.

EXPLAIN (VERBOSE,ANALYZE,BUFFERS) SELECT client_id,
CASE WHEN
(SELECT program_type_code FROM reg_spc WHERE target_date() BETWEEN reg_spc_date AND COALESCE(reg_spc_date_end,target_date()) AND client_id=tro.client_id LIMIT 1)
ILIKE 'SSP%' THEN   COALESCE((SELECT staff_id FROM staff_employment_current WHERE staff_position_code='COORD_PROP' AND agency_project_code='SSP' LIMIT 1),(SELECT staff_id FROM staff_employment_current WHERE staff_position_code='MGRPROJ' AND agency_project_code='SSP' LIMIT 1))
ELSE   (SELECT staff_inspector FROM tbl_residence_own ro LEFT JOIN l_housing_project USING (housing_project_code) WHERE client_id=5538 AND target_date() BETWEEN residence_date AND COALESCE(residence_date_end,target_date()) AND NOT ro.is_deleted LIMIT 1)
END
FROM tbl_residence_own tro;

EXPLAIN (VERBOSE,ANALYZE,BUFFERS) SELECT client_id,
CASE WHEN
(SELECT program_type_code FROM reg_spc WHERE target_date() BETWEEN reg_spc_date AND COALESCE(reg_spc_date_end,target_date()) AND client_id=tro.client_id LIMIT 1)
ILIKE 'SSP%' THEN
   COALESCE((SELECT staff_id FROM staff_employment_current WHERE staff_position_code='COORD_PROP' AND agency_project_code='SSP' LIMIT 1),(SELECT staff_id FROM staff_employment_current WHERE staff_position_code='MGRPROJ' AND agency_project_code='SSP' LIMIT 1))
ELSE
   (SELECT staff_inspector FROM tbl_residence_own ro LEFT JOIN l_housing_project USING (housing_project_code) WHERE client_id=tro.client_id AND target_date() BETWEEN residence_date AND COALESCE(residence_date_end,target_date()) AND NOT ro.is_deleted LIMIT 1)
END
FROM tbl_residence_own tro;