ioguix@erg:~$ dropdb correl 
ioguix@erg:~$ createdb correl
ioguix@erg:~$ psql -qtX correl 
correl=# CREATE TABLE correl AS SELECT (i-1)%2 AS i, i%2 AS j FROM generate_series(1,100000) AS i;

correl=# ANALYZE correl ;

correl=# EXPLAIN ANALYZE SELECT * FROM correl WHERE i = 1 AND j = 1;
 Seq Scan on correl  (cost=0.00..1943.00 rows=25000 width=8) (actual time=21.898..21.898 rows=0 loops=1)
   Filter: ((i = 1) AND (j = 1))
   Rows Removed by Filter: 100000
 Planning time: 0.356 ms
 Execution time: 21.937 ms

correl=# CREATE FUNCTION fix_correl(int, int) RETURNS bool AS '
BEGIN RETURN $1 = 1 AND $2 = 1; END '
IMMUTABLE
CALLED ON NULL INPUT
LANGUAGE plpgsql;

correl=# CREATE INDEX ON correl ( fix_correl(i, j) );

correl=# ANALYZE correl ;

correl=# EXPLAIN ANALYZE SELECT * FROM correl WHERE fix_correl(i, j);
 Index Scan using correl_fix_correl_idx on correl  (cost=0.29..4.56 rows=33333 width=8) (actual time=0.053..0.053 rows=0 loops=1)
   Index Cond: (fix_correl(i, j) = true)
   Filter: fix_correl(i, j)
 Planning time: 0.421 ms
 Execution time: 0.102 ms

correl=# SELECT * FROM pg_stats WHERE tablename ~ '^correl_';
schemaname             | public
tablename              | correl_fix_correl_idx
attname                | fix_correl
inherited              | f
null_frac              | 0
avg_width              | 1
n_distinct             | 1
most_common_vals       | {f}
most_common_freqs      | {1}
histogram_bounds       | 
correlation            | 1
most_common_elems      | 
most_common_elem_freqs | 
elem_count_histogram   | 


correl=# CREATE INDEX ON correl ( (i + j) );

correl=# ANALYZE correl ;

correl=# EXPLAIN ANALYZE SELECT * FROM correl WHERE ( i + j ) = 2;
 Index Scan using correl_expr_idx on correl  (cost=0.29..4.31 rows=1 width=8) (actual time=0.027..0.027 rows=0 loops=1)
   Index Cond: ((i + j) = 2)
 Planning time: 0.175 ms
 Execution time: 0.076 ms

correl=# CREATE FUNCTION fix_correl_add(int, int) RETURNS int AS '
BEGIN RETURN $1 + $2 ; END '
IMMUTABLE
CALLED ON NULL INPUT
LANGUAGE plpgsql;

correl=# CREATE INDEX ON correl ( fix_correl_add( i, j ) );

correl=# ANALYZE correl ;

correl=# EXPLAIN ANALYZE SELECT * FROM correl WHERE fix_correl_add( i, j ) = 2;
 Index Scan using correl_fix_correl_add_idx on correl  (cost=0.29..4.31 rows=1 width=8) (actual time=0.052..0.052 rows=0 loops=1)
   Index Cond: (fix_correl_add(i, j) = 2)
 Planning time: 0.462 ms
 Execution time: 0.102 ms

correl=# SELECT * FROM pg_stats WHERE tablename ~ '^correl_';
schemaname             | public
tablename              | correl_fix_correl_idx
attname                | fix_correl
inherited              | f
null_frac              | 0
avg_width              | 1
n_distinct             | 1
most_common_vals       | {f}
most_common_freqs      | {1}
histogram_bounds       | 
correlation            | 1
most_common_elems      | 
most_common_elem_freqs | 
elem_count_histogram   | 
-----------------------+--------------------------
schemaname             | public
tablename              | correl_expr_idx
attname                | expr
inherited              | f
null_frac              | 0
avg_width              | 4
n_distinct             | 1
most_common_vals       | {1}
most_common_freqs      | {1}
histogram_bounds       | 
correlation            | 1
most_common_elems      | 
most_common_elem_freqs | 
elem_count_histogram   | 
-----------------------+--------------------------
schemaname             | public
tablename              | correl_fix_correl_add_idx
attname                | fix_correl_add
inherited              | f
null_frac              | 0
avg_width              | 4
n_distinct             | 1
most_common_vals       | {1}
most_common_freqs      | {1}
histogram_bounds       | 
correlation            | 1
most_common_elems      | 
most_common_elem_freqs | 
elem_count_histogram   |