Calculate battery life when LEDs are different voltage to the battery.
3.84 W at 1.2 V is 3.2 A, more than one AAA NiMH battery can muster. This datasheet only shows up to 2 A, and the curve isn't pretty.

Note that at such a high load, it's not a 1.2 V battery at all. Internal resistance is significant, which also means it'll heat up.