How good is the analysis engine?

Is it worth getting premium for?

it's pretty good, You have diamond membership, always do in deepth max level, it will tell you many things above your move and what cud have been done to improve ur game.

No. It's not worth paying premium for the analysis - though there are other reasons (videos, etc.) for paying premium. The deep analysis is very sparse. Simply get Lucas Chess (freeware) at: https://lucaschess.pythonanywhere.com/

I have only used the laptop version but the portable version may do as well on smartphones.

It comes with either Stockfish 8 or Stockfish 9 built-in (I don't know if the latest version has the newest version). If it doesn't have Stockfish 9 (freeware), you can download it and then use it seamlessly with Lucas as an external engine: https://stockfishchess.org/download/

Save your game as a pgn file on your computer/phone and then read the pgn into Lucas Chess.

You can then analyze much deeper than chess.com's deepest analysis on Lucas Chess and, for every move you can call up a list of Stockfish's preferred moves and their continuations in value order.

I also find Lucas Chess's estimation of the level of play to be much more realistic than chess.com's CAPS system.

Thanks Mick - I got the free trial for premium.

May I ask - what's your main reason for using premium?

Lucas Chess is excellent, I would pay for it. Another option is Fritz - it has quite "verbose" analysis. But you have to cough for it, of course.

I'm using premium mainly for the videos.  I like some of the series that are more concise and focused than many of the YouTube videos - though I like some of them as well - especially IM Danny Rensch's pattern recognition videos.  A lot of my chess improvement over the past year has been due to improved pattern recognition.

People don't use premium for analysis only, you can gain excess to unlimited videos, tactics, lessons,etc

This way chess.com configured the engine for a fast analysis is simply the best way to seriously improve I have ever seen, and it is good at any level. I personally have improved a lot thanks to the combination of new patterns you can get in short time. 
Obviously it is has to be combined with all the other tools you need to put in place to learn, but it can help you a lot!