What is the difference between these?

To me, these three queries seem identical... why doesn't the first one
(simplest to understand and write) go the same speed as the third one?

I'll I'm trying to do is get statistics for one day (in this case,
today) summarized. Table has ~25M rows. I'm using postgres 7.3.? on
rh linux 7.3 (note that i think the difference between the first two
might just be related to the data being in memory for the second
query).

EXPLAIN ANALYZE
select count(distinct sessionid) from usage_access where atime >
date_trunc('day', now());
QUERY PLAN
----------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=933439.69..933439.69 rows=1 width=4) (actual
time=580350.43..580350.43 rows=1 loops=1)
-> Seq Scan on usage_access (cost=0.00..912400.11 rows=8415831
width=4) (actual time=580164.48..580342.21 rows=2964 loops=1)
Filter: (atime > date_trunc('day'::text, now()))
Total runtime: 580350.65 msec
(4 rows)

EXPLAIN ANALYZE
select count(distinct sessionid) from (select * from usage_access
where atime > date_trunc('day', now())) as temp;
QUERY PLAN
----------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=933439.69..933439.69 rows=1 width=4) (actual
time=348012.85..348012.85 rows=1 loops=1)
-> Seq Scan on usage_access (cost=0.00..912400.11 rows=8415831
width=4) (actual time=347960.53..348004.68 rows=2964 loops=1)
Filter: (atime > date_trunc('day'::text, now()))
Total runtime: 348013.10 msec
(4 rows)

EXPLAIN ANALYZE
select count(distinct sessionid) from usage_access where atime
between date_trunc('day', now()) and date_trunc('day', now()) + '1
day'::interval;
QUERY PLAN
--------------------------------------------------------------------------------------------------------------------------------------------------
Aggregate (cost=89324.98..89324.98 rows=1 width=4) (actual
time=27.84..27.84 rows=1 loops=1)
-> Index Scan using usage_access_atime on usage_access
(cost=0.00..89009.39 rows=126237 width=4) (actual time=0.51..20.37
rows=2964 loops=1)
Index Cond: ((atime >= date_trunc('day'::text, now())) AND
(atime <= (date_trunc('day'::text, now()) + '1 day'::interval)))
Total runtime: 28.11 msec
(4 rows)

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