PostgreSQL several COUNT DISTINCT in same query with GROUP BY on other field

i am looking for elegant way to write PostgreSQL version of this query:

SELECT count(distinct a,b) / count(distinct c,d) FROM t1 GROUP BY e; 

It can be done via CONCAT function, but it this case i get huge performance drop.

Each count distinct can be written in this way:

SELECT count(*), e FROM (SELECT a, b, e FROM t1 GROUP BY a, b, e) as tmp GROUP BY e; 

AND

SELECT count(*), e FROM (SELECT c, d, e FROM t1 GROUP BY c, d, e) as tmp GROUP BY e; 

But i can't find how to combine them into one query to get final result

Here is create table to test syntax:

CREATE TABLE t1 ( a int, b int, c int, d int, e int );