"Looping" the same SQL query for all entries grouped by date - mysql

Question

I have a table like this:
+------------+-----------+------+----+
| date | player_id | rank | hp |
+------------+-----------+------+----+
| 2021-01-01 | 1 | 1 | 39 |
| 2021-01-01 | 5 | 2 | 20 |
| 2021-01-01 | 2 | 3 | 12 |
| 2021-01-01 | 3 | 4 | 48 |
| 2021-01-01 | 4 | 5 | 25 |
| 2021-01-02 | 1 | 2 | 42 |
| 2021-01-02 | 2 | 1 | 38 |
| 2021-01-02 | 3 | 4 | 21 |
| 2021-01-02 | 4 | 3 | 35 |
| 2021-01-02 | 5 | 5 | 28 |
| 2021-01-03 | 1 | 5 | 38 |
| 2021-01-03 | 3 | 2 | 31 |
| 2021-01-03 | 2 | 3 | 26 |
| 2021-01-03 | 4 | 4 | 22 |
| 2021-01-03 | 5 | 1 | 19 |
+------------+-----------+------+----+
When I use the following SQL code:
SELECT * FROM
(SELECT * FROM `players` WHERE date='2021-01-01' ORDER BY rank ASC LIMIT 3) highest_rank
ORDER BY hp DESC LIMIT 2
The result will be this:
+------------+-----------+------+----+
| date | player_id | rank | hp |
+------------+-----------+------+----+
| 2021-01-01 | 1 | 1 | 39 |
| 2021-01-01 | 5 | 2 | 20 |
+------------+-----------+------+----+
My problem is the result is only for date='2021-01-01'. I want to do this for every day in the database. Ultimately, I want the result to look like this:
+------------+-----------+------+----+
| date | player_id | rank | hp |
+------------+-----------+------+----+
| 2021-01-01 | 1 | 1 | 39 |
| 2021-01-01 | 5 | 2 | 20 |
| 2021-01-02 | 1 | 2 | 42 |
| 2021-01-02 | 2 | 1 | 38 |
| 2021-01-03 | 3 | 2 | 31 |
| 2021-01-03 | 2 | 3 | 26 |
+------------+-----------+------+----+
How can this be done? I'm using MySQL/MariaDB if that makes any difference.

Answer 1

Problem solved. Credit goes to sticky bit in the comment section that provided a solution that almost worked. He retracted the suggestion because it wasn't the final solution, I think. But I tinkered with it and got it to work. Thank you, sticky bit!
For anyone interested in the solution:
SELECT date, player_id, rank, hp
FROM
(
SELECT *,
row_number() OVER (PARTITION BY date
ORDER BY hp DESC) h
FROM
(
SELECT *,
row_number() OVER (PARTITION BY date
ORDER BY rank ASC) r
FROM players
) x
WHERE r<=3
) y
WHERE h<=2