One of purposes of the STACK_GLOBAL opcode introduced in pickle protocol 4 is to avoid repeating module name for different globals of the same module.

>>> pickletools.dis(pickletools.optimize(pickle.dumps([sys.getsizeof, sys.intern], 4)))
    0: \x80 PROTO      4
    2: \x95 FRAME      33
   11: ]    EMPTY_LIST
   12: (    MARK
   13: \x8c     SHORT_BINUNICODE 'sys'
   18: \x94     MEMOIZE    (as 0)
   19: \x8c     SHORT_BINUNICODE 'getsizeof'
   30: \x93     STACK_GLOBAL
   31: h        BINGET     0
   33: \x8c     SHORT_BINUNICODE 'intern'
   41: \x93     STACK_GLOBAL
   42: e        APPENDS    (MARK at 12)
   43: .    STOP
highest protocol among opcodes = 4

But this doesn't work with the itertools module.

>>> pickletools.dis(pickletools.optimize(pickle.dumps([itertools.chain, itertools.accumulate], 4)))
    0: \x80 PROTO      4
    2: \x95 FRAME      47
   11: ]    EMPTY_LIST
   12: (    MARK
   13: \x8c     SHORT_BINUNICODE 'itertools'
   24: \x8c     SHORT_BINUNICODE 'chain'
   31: \x93     STACK_GLOBAL
   32: \x8c     SHORT_BINUNICODE 'itertools'
   43: \x8c     SHORT_BINUNICODE 'accumulate'
   55: \x93     STACK_GLOBAL
   56: e        APPENDS    (MARK at 12)
   57: .    STOP
highest protocol among opcodes = 4

That is because the __module__ attribute of itertools members is not interned.

>>> sys.getsizeof.__module__ is sys.intern.__module__
True
>>> itertools.chain.__module__ is itertools.chain.__module__
False

In addition to inefficient pickle this perhaps leads to small performance hit on accessing the __module__ attribute or using its value as dictionary key.