Is there a PL/SQL function to count the number of n subtypes of a super type?

Is there a function in PL/SQL that can count the number of n subtypes of a table (supertype)?

I've tried the following:

select
    count(distinct value(t1))
from table t1;

select
    count(distinct treat(value(t1))
from table t1;

Basically, if a table has 6 subtypes, I would like a query that could output 6.

Oracle Setup:

CREATE TYPE parent_type AS OBJECT( id NUMBER ) NOT FINAL;
CREATE TYPE child1_type UNDER parent_type ( c1 NUMBER );
CREATE TYPE child2_type UNDER parent_type ( c2 NUMBER ) NOT FINAL;
CREATE TYPE child3_type UNDER child2_type ( c3 NUMBER );

CREATE TABLE test_data ( value parent_type );

INSERT INTO test_data ( value )
  SELECT parent_type( 1 ) FROM DUAL UNION ALL
  SELECT child1_type( 2, 1 ) FROM DUAL UNION ALL
  SELECT child1_type( 3, 1 ) FROM DUAL UNION ALL
  SELECT child1_type( 4, 1 ) FROM DUAL UNION ALL
  SELECT child2_type( 5, 2 ) FROM DUAL UNION ALL
  SELECT child2_type( 6, 2 ) FROM DUAL UNION ALL
  SELECT child3_type( 7, 3, 1 ) FROM DUAL UNION ALL
  SELECT child3_type( 8, 3, 1 ) FROM DUAL UNION ALL
  SELECT child3_type( 9, 3, 1 ) FROM DUAL;

Query 1:

If you know the type hierarchy then you can build a query manually using the fact that TREAT( object AS type ) will return NULL if the object you are passing is not of that type and can use a CASE statement and start from the leaves of the hierarchy tree and process the types from deepest inheritance depth through to the parent type:

SELECT COUNT( DISTINCT
         CASE
         WHEN TREAT( value AS child3_type ) IS NOT NULL
           THEN 'child3_type' -- deepest subtype
         WHEN TREAT( value AS child2_type ) IS NOT NULL
           THEN 'child2_type' -- supertype of child3_type, subtype of parent_type
         WHEN TREAT( value AS child1_type ) IS NOT NULL
           THEN 'child1_type' -- subtype of parent_type
         ELSE 'parent_type'
         END
       ) AS num_types
FROM   test_data

Query 2:

If you have access to the SYS.ANYDATA type then you can get the type of the object:

SELECT COUNT(
         DISTINCT
         SYS.ANYDATA.getTypeName(
           SYS.ANYDATA.convertObject( value )
         )
       ) AS num_types
FROM   test_data

Output:

Both give the same output:

| NUM_TYPES |
| --------: |
|         4 |

db<>fiddle here