The optimization process and recommendations:

1. Avoid Correlated Subqueries (query line: 5): A correlated subquery is a subquery that contains a reference (column: updated_at) to a table that also appears in the outer query. Usually correlated queries can be rewritten with a join clause, which is the best practice. The database optimizer handles joins much better than correlated subqueries. Therefore, rephrasing the query with a join will allow the optimizer to use the most efficient execution plan for the query.
2. Avoid Correlated Subqueries (query line: 12): A correlated subquery is a subquery that contains a reference (column: threeable_id) to a table that also appears in the outer query. Usually correlated queries can be rewritten with a join clause, which is the best practice. The database optimizer handles joins much better than correlated subqueries. Therefore, rephrasing the query with a join will allow the optimizer to use the most efficient execution plan for the query.
3. Avoid Selecting Unnecessary Columns (query line: 13): Avoid selecting all columns with the '*' wildcard, unless you intend to use them all. Selecting redundant columns may result in unnecessary performance degradation.
4. Avoid Subqueries (query line: 15): We advise against using subqueries as they are not optimized well by the optimizer. Therefore, it's recommended to join a newly created temporary table that holds the data, which also includes the relevant search index.
5. Create Optimal Indexes (modified query below): The recommended indexes are an integral part of this optimization effort and should be created before testing the execution duration of the optimized query.
6. Explicitly ORDER BY After GROUP BY (modified query below): By default, the database sorts all 'GROUP BY col1, col2, ...' queries as if you specified 'ORDER BY col1, col2, ...' in the query as well. If a query includes a GROUP BY clause but you want to avoid the overhead of sorting the result, you can suppress sorting by specifying 'ORDER BY NULL'.

Optimal indexes for this query:

ALTER TABLE `threes` ADD INDEX `threes_idx_updated_at` (`updated_at`);
ALTER TABLE `threes` ADD INDEX `threes_idx_deleted_at_threeable_threeable` (`deleted_at`,`threeable_id`,`threeable_type`);
ALTER TABLE `twos` ADD INDEX `twos_idx_id` (`id`);

The optimized query:

SELECT
        twos.id,
        threes.id 
    FROM
        (SELECT
            twos.id twoId,
            MAX(th.updated_at) threeMaxUA 
        FROM
            twos 
        LEFT JOIN
            (
                SELECT
                    th.* 
                FROM
                    (SELECT
                        threes.threeable_id,
                        threes.threeable_type,
                        MAX(updated_at) AS updated_at 
                    FROM
                        threes 
                    WHERE
                        threes.deleted_at IS NULL 
                    GROUP BY
                        threes.threeable_id,
                        threes.threeable_type 
                    ORDER BY
                        NULL) thmax 
                LEFT JOIN
                    threes pr 
                        ON (
                            th.threeable_id = thmax.threeable_id 
                            AND th.updated_at = thmax.updated_at 
                            AND th.threeable_type = thmax.threeable_type
                        ) 
                GROUP BY
                    th.threeable_id,
                    th.threeable_type 
                ORDER BY
                    NULL) th 
                        ON ((th.threeable_id = twos.id 
                        AND th.threeable_type = 'App\\Two') 
                        OR (th.threeable_id = twos.product_id 
                        AND th.threeable_type = 'App\\One')) 
                GROUP BY
                    twos.id 
                ORDER BY
                    NULL
            ) twthmax 
        LEFT JOIN
            twos 
                ON twos.id = twthmax.twoId 
        LEFT JOIN
            threes 
                ON (
                    twthmax.threeMaxUA = threes.updated_at 
                    AND (
                        (
                            threes.threeable_id = twos.id 
                            AND threes.threeable_type = 'App\\Two'
                        ) 
                        OR (
                            threes.threeable_id = twos.product_id 
                            AND threes.threeable_type = 'App\\One'
                        )
                    )
                )