Both sentences mean the exact same thing. However, the term work out can mean physically working out, gym. So in that case you would say, I work out at home. " AT" is needed to mean you are working out at your house, not from your house. You still would not say I work out from home to mean you "workout " as in doing gym work. So its tricky. So if you work out from home, or work from home, it means the exact same thing. A small percent of people will say work out from home, majority will just say work from home. But working out at home, is a different meaning, that is doing gym workout at home.