I gave up on productivity long ago. It depends on the type of work that you do. If I am let's say on the assembly line and everything is already thought of and I have to follow well written guides, then I could try to be productive, avoid distractions and so on.
On my job I have to research complex problems, that you can't simply google them and find an answer. It takes time to design a possible solution, trial and error, a lot of thinking and observing and in the end you feel that you have hit a wall. In such cases I simply need a break and to think for something else for a while. It is also very hard to put an estimate and set a deadline for a such thing, so productivity is the least of my problems.