create table why_u_no_use_index (id uuid, long_text text);
insert into why_u_no_use_index (select gen_random_uuid(), random() * 100 from generate_series(1, 100000));
create index null_check on why_u_no_use_index((long_text is null));
explain analyze select * from why_u_no_use_index where long_text is null limit 100;

# postgres
postgres=# explain analyze select * from why_u_no_use_index where long_text is null limit 100;
                                                              QUERY PLAN                                                              
--------------------------------------------------------------------------------------------------------------------------------------
 Limit  (cost=0.29..4.31 rows=1 width=32) (actual time=0.075..0.075 rows=0 loops=1)
   ->  Index Scan using null_check on why_u_no_use_index  (cost=0.29..4.31 rows=1 width=32) (actual time=0.074..0.074 rows=0 loops=1)
         Index Cond: ((long_text IS NULL) = true)
         Filter: (long_text IS NULL)
 Planning Time: 0.168 ms
 Execution Time: 0.093 ms
(6 rows)

# cockroachdb
root@:26257/defaultdb> explain analyze select * from why_u_no_use_index@null_check where long_text is null limit 100;
                             info
---------------------------------------------------------------
  planning time: 579µs
  execution time: 12.5s
  distribution: full
  vectorized: true
  rows read from KV: 200,000 (9.0 MiB)
  cumulative time spent in KV: 12.5s
  maximum memory usage: 10 MiB
  network usage: 0 B (0 messages)

  • limit
  │ nodes: n1
  │ actual row count: 0
  │ count: 100
  │
  └── • filter
      │ nodes: n1
      │ actual row count: 0
      │ filter: long_text IS NULL
      │
      └── • index join
          │ nodes: n1
          │ actual row count: 100,000
          │ KV time: 12.1s
          │ KV contention time: 0µs
          │ KV rows read: 100,000
          │ KV bytes read: 5.3 MiB
          │ estimated max memory allocated: 6.4 MiB
          │ estimated max sql temp disk usage: 0 B
          │ table: why_u_no_use_index@why_u_no_use_index_pkey
          │
          └── • scan
                nodes: n1
                actual row count: 100,000
                KV time: 477ms
                KV contention time: 0µs
                KV rows read: 100,000
                KV bytes read: 3.6 MiB
                estimated max memory allocated: 3.7 MiB
                missing stats
                table: why_u_no_use_index@null_check
                spans: FULL SCAN
(41 rows)


Time: 12.541s total (execution 12.540s / network 0.001s)