A redundant type(r) = 'P' check makes a statically typed relationship query about 6x slower

I found that adding WHERE type(r) = 'P' to a relationship already matched as [r:P] makes the query about six times slower. The condition is always true, and both queries return the same count.

• Apache AGE Version: 1.7.0
• PostgreSQL Version: 18.1
• Operating System: macOS 27.0 arm64
• Installation Method: official apache/age Docker image
• API/Driver: PostgreSQL wire protocol / Psycopg 3.3.4

Steps to reproduce

1. Load AGE and create a fresh graph:

   LOAD 'age';
   SET search_path = ag_catalog, "$user", public;
   SELECT ag_catalog.create_graph('relationship_type_guard_perf');

2. Create 20,000 relationships of type P:

   SELECT * FROM ag_catalog.cypher('relationship_type_guard_perf', $$
     UNWIND range(1, 20000) AS i
     CREATE (:X {id: i})-[:P {id: i}]->(:Y {id: i})
     RETURN count(*) AS created
   $$) AS (created agtype);

3. Refresh the label statistics:

   ANALYZE relationship_type_guard_perf."X";
   ANALYZE relationship_type_guard_perf."Y";
   ANALYZE relationship_type_guard_perf."P";

4. Run query A:

   SELECT * FROM ag_catalog.cypher('relationship_type_guard_perf', $$
     MATCH (:X)-[r:P]->(:Y)
     RETURN count(*) AS c
   $$) AS (c agtype);

5. Run query B, which only adds a condition already guaranteed by [r:P]:

   SELECT * FROM ag_catalog.cypher('relationship_type_guard_perf', $$
     MATCH (:X)-[r:P]->(:Y)
     WHERE type(r) = 'P'
     RETURN count(*) AS c
   $$) AS (c agtype);

6. Prefix both queries with EXPLAIN (ANALYZE, BUFFERS) to inspect their plans.

Expected behavior

Both queries should return c = 20000. Since [r:P] already limits r to type P, query B should not need to rebuild each relationship value and check its type again.

Actual behavior

Both queries return c = 20000, but query B is consistently slower. Each independent instance ran 12 alternating comparisons, and query B was slower in all of them:

The slow plan applies this filter while scanning the P relationship table:

Filter: (age_type(_agtype_build_edge(...)) = '"P"'::agtype)

The fast plan scans the same P table without that filter.