Should I exercise when tired?

Went to sleep way too late last night and got about ½ as many hours of sleep as normal. Work is a 9–5 desk job and I am both mentally and physically tired & dragging. M, W, F I normally go to the gym for 30 mins on treadmill & a couple of machines (no free weights) for about an hour workout. Drive from work to gym is about 25 mins & from gym to home about 20 mins. Do you think I should push myself to workout today even though I’m so tired or should I skip today?