Watch app has just 3 screens.
iPhone app here.
I'm new to the whole sleep tracking thing, so I don't yet understand what light sleep or deep sleep really are, but as for what I can say about this app, I think it's pretty much got things exactly right when it comes to tracking how long it is until I fall asleep, and when I'm waking back up.
I usually turn it on and read something for a few minutes before I go to sleep. I can just about always go to sleep right away. I can remember around how long I was looking at something before I go to sleep, because I'm usually looking at something on the computer, so I glance at the time before turning it off. This is how I inadvertently found out how accurate that feature of the app is.
I was also pleasantly surprised to find out that I checked the report one morning after I turned off the app, and the app knew that I woke up during the sleep period.
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iPad Pro
AND Surface Pro 4?!