Oh my god, think of what this would do to commerce, in terms of a capitalist society.
Suddenly, you can take a drug that decreases your need for sleep by 50%. People only need 4h of sleep per night now, for a full nights' sleep - 3h, if you're willing to skimp a little, 2h isn't unheard of (in the way that only getting 4h of sleep a night, now, isn't unheard of either).
Suddenly, there's a significant advantage in the hands of everyone willing to take this drug. Students are expected to study more and harder, because they don't need 8h of sleep every night. Entrance exams to schools get more difficult. Software developers are now enticed to work longer hours - longer hours than they already are. Labor / shift workers (hospitality / food industry) are expected to work longer shifts, and they have to, because businesses have to be open longer because more people are awake for more of the day.
Now, also, you have to consider: this is just sleep, in terms of brain repair. Your body has to put itself back together every night, too - repairing microscopic muscle tears, fixing bruises, etc etc etc. Your body would probably start slowly falling apart on 2-3h of sleep per night, even if your mind was fully rested.
I really, really hope this doesn't happen.