It occurs to me that when a person is tired, they should probably rest (crazy, I know). When you're not feeling well, when your head is cloudy and you can't concentrate, there's not much point to sitting at your desk - you should probably go home.
But often, we're reluctant to do that, for fear of looking like a slacker. Never mind that you're not accomplishing anything by staying at your desk until "quitting time." Appearances must be kept up. In the minds of some, it's more important to maintain the impression of doing work than to actually do the work (or to do the smart thing and go home).
As for me, I try to be the guy who goes home, boldly and unapologetically. That last 30 or 45 minutes wasn't going to be productive anyway - I might as well go get some rest so I can come back tomorrow (hopefully) feeling better.