Python:
Score: 2↑↑11 / 830584 (Knuth up arrow notation)
print True<<(True<<(True<<(True<<(True<<(True<<(True<<(True<<(True<<(True<<True<<True)))))))))
Probably no computer has enough memory to successfully run this, but that's not really the program's fault. With the minimum system requirements satisfied, it does work.
Yes, this is doing bit shifting on boolean values. True gets coerced to 1 in this context. Python has arbitrary length integers.