ORA-07445: exception encountered: core dump [__intel_new_memcpy()+382] [SIGILL] [ADDR:0x3FE5CAE] [PC:0x3FE5CAE] [Illegal operand] 
Searching metalink didn't get us anywhere, so we opened a TAR (or iTar, or SR, or ServReq, or whatever the heck they are calling them these days). While Oracle Support was looking at the issue, I looked at the query generating the error:
SELECT nvl(t.value, null) FROM table t WHERE t.id = 12345;
Huh? If the value is null, substitute a null? WTF?
SELECT t.value FROM table t WHERE t.id = 12345;
...and the error goes away.
Is it a bug on Oracle's side? Sure.
Is it a stupid thing to do on our side? You betcha.