Postgres 13

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.
set enable_bitmapscan=false
create table demo (id bigint, username text)
insert into demo select n,'Number'||to_hex(n) from generate_series(1,1000) n
1000 rows affected

vacuum demo
select * from demo where username='Number42'

id
username

66
Number42

explain analyze select * from demo where upper(username)='NUMBER42'

QUERY PLAN

Seq Scan on demo  (cost=0.00..22.00 rows=5 width=40) (actual time=0.097..0.444 rows=1 loops=1)

  Filter: (upper(username) = 'NUMBER42'::text)

  Rows Removed by Filter: 999

Planning Time: 0.025 ms

Execution Time: 0.454 ms

explain analyze select upper(username) from demo where upper(username)='NUMBER42'

QUERY PLAN

Seq Scan on demo  (cost=0.00..22.01 rows=5 width=32) (actual time=0.033..0.351 rows=1 loops=1)

  Filter: (upper(username) = 'NUMBER42'::text)

  Rows Removed by Filter: 999

Planning Time: 0.024 ms

Execution Time: 0.361 ms

create index demo_upper on demo( (upper(username)) )
explain analyze select upper(username) from demo where upper(username)='NUMBER42'

QUERY PLAN

Index Scan using demo_upper on demo  (cost=0.28..20.38 rows=5 width=32) (actual time=0.043..0.045 rows=1 loops=1)

  Index Cond: (upper(username) = 'NUMBER42'::text)

Planning Time: 0.272 ms

Execution Time: 0.067 ms

create index demo_upper_covering on demo( (upper(username))) include (username )
explain analyze select upper(username) from demo where upper(username)='NUMBER42'

QUERY PLAN

Index Only Scan using demo_upper_covering on demo  (cost=0.28..4.38 rows=5 width=32) (actual time=0.044..0.046 rows=1 loops=1)

  Index Cond: ((upper(username)) = 'NUMBER42'::text)

  Heap Fetches: 0

Planning Time: 0.206 ms

Execution Time: 0.066 ms

alter table demo add column upper_username text generated always as (upper(username)) stored
create index demo_upper_stored on demo( upper_username )
vacuum demo
explain analyze select upper_username from demo where upper_username='NUMBER42'

QUERY PLAN

Index Only Scan using demo_upper_stored on demo  (cost=0.28..4.36 rows=5 width=32) (actual time=0.046..0.047 rows=1 loops=1)

  Index Cond: (upper_username = 'NUMBER42'::text)

  Heap Fetches: 0

Planning Time: 0.123 ms

Execution Time: 0.066 ms