First remember that attack speed is a value from 0-1024. At 0 attack speed, your weapons don't recharge at all. At 1024, they recharge instantly. Now, if you hold an item in your off hand with -1023.9 Attack Speed and an item in your main hand with +1020 attack speed, since your Base is 4.0, you should end up with 0.1 attack speed (4 -1023.9 + 1020 = 0.1), which is a legal value, so we're good. What actually happens is you somehow end up with 4 attack speed (Well actually I can't read the exact value, but it certainly looks and feels exactly the same as using your fist). I haven't any idea how this occurs. Thing is though, if you switch hands so that your off hand holds the +1020 attack speed item, and main hand holds the -1023.9 attack speed item, it works as intended, giving the player 0.1 attack speed (It takes 10 seconds for attack strength bar to refill). Stranger still, if you then hit f (Swap hands key) to swap to the first setup, it will then give you 0 attack speed, and the attack meter will remain empty. If you select a different item and then the +1020 AS item again, you get returned to 4 AS.

It seems there's an issue with the max and min values being checked in between applying all of the operations on various items. This leads to some inconsistent and unexpected behaviour resulting from the order in which items are held and selected.