CREATE TABLE test(a int);

CREATE OR REPLACE FUNCTION is_odd(a int)
    RETURNS boolean AS
$$
BEGIN
    RETURN a % 2 = 0;
END;
$$
LANGUAGE 'plpgsql' IMMUTABLE STRICT

CREATE OR REPLACE FUNCTION is_odd_int(a int)
    RETURNS int AS
$$
BEGIN
    RETURN a % 2;
END;
$$
LANGUAGE 'plpgsql' IMMUTABLE STRICT

insert into test(a) values(1)

insert into test(a) values(2)

create index test_is_odd on test  USING btree(is_odd(a));

create index test_is_odd_int on test  USING btree(is_odd_int(a));

set enable_seqscan=false;

set enable_bitmapscan=false;

CREATE OR REPLACE FUNCTION is_odd(a int)
    RETURNS boolean AS
$$
BEGIN
    perform pg_sleep(0.5);
    RETURN a % 2 = 0;
END;
$$
LANGUAGE 'plpgsql' IMMUTABLE STRICT

CREATE OR REPLACE FUNCTION is_odd_int(a int)
    RETURNS int AS
$$
BEGIN
    perform pg_sleep(0.5);
    RETURN a % 2;
END;
$$
LANGUAGE 'plpgsql' IMMUTABLE STRICT


explain analyse
select * from test where is_odd(a) = true; -- 500ms

explain analyse
select * from test where is_odd(a) = false; -- 500ms

explain analyse
select * from test where is_odd_int(a) = 0; -- 0ms

explain analyse
select * from test where is_odd_int(a) = 1; -- 0ms