Oracle 11.2 Explain Plan takes too long

I’m using Oracle 11.2 SE on a 16GB Xeon E3 Linux machine as well as 11.2 XE on a 8GB i7 Win8 machine:

SELECT banner FROM v$version:

Oracle Database 11g Release 11.2.0.4.0 - 64bit Production
PL/SQL Release 11.2.0.4.0 - Production
"CORE   11.2.0.4.0  Production"
TNS for Linux: Version 11.2.0.4.0 - Production
NLSRTL Version 11.2.0.4.0 - Production

and

Oracle Database 11g Express Edition Release 11.2.0.2.0 - Production
PL/SQL Release 11.2.0.2.0 - Production
"CORE   11.2.0.2.0  Production"
TNS for 32-bit Windows: Version 11.2.0.2.0 - Production
NLSRTL Version 11.2.0.2.0 - Production

Both systems suffer from the same problem:
I have a complicated SELECT (120 steps in EXPLAIN PLAN) for a right now pretty empty schema (20 MB in total):

SELECT segment_type, COUNT(*) AS objectcount,
       SUM(bytes / 1024 / 1024) AS MB FROM user_segments GROUP BY segment_type;

LOBINDEX    1   0,0625
LOBSEGMENT  1   2
TABLE       55  6,4375
INDEX       204 12,75

Table stats are gathered with:

DBMS_STATS.GATHER_TABLE_STATS(ownname=>USER, tabname => loop_tablesnames,
   estimate_percent=>100, method_opt=>'FOR ALL COLUMNS', cascade=>true, force=>true);

The EXPLAIN PLAN for the statement leading to 120 steps (these are expected) takes approx 7sec on the linux machine and 22sec on the win8 machine.

The installs are basic, no changes to the Oracle configuration have been done.

As my SQLs are generated and do not use parameter binding, almost every statement is hard-parsed leading to the same delay for statement execution. Once no hard parse is needed, the statement executes within milliseconds.

For less complicated statements, the EXPLAIN PLAN is fast.

Is there anything I can do to speed up the EXPLAIN PLAN and the hard parse step (I’d think that the solution for EXPLAIN PLAN will also solve the other)?

Thank you & best regards,
Blama