http://lifehacker.com/how-to-stream-the-2016-olympics-online-no-cable-requir-1784852516
You have to go through a fair number of screens to get it going. but the free trial gives you log-in credentials for the live steaming and replays.
I did did not have to re-login this morning.
And it patches over to my TV better than the Sling did.
By the way, the PlayStation site might convince you that it won’t allow you to stream via computer, but you can. Just go to the NBC site and log in when it asks you to after about 30 minutes free.