Concrete bathtub - smooth finishing

I made a concrete bathtub. I love it. It looks great.

It's dug into the earth, with a layer of foam insulation and then ferrocement work, layer after layer to make it smooth.

The final layer of concrete brought it to about the level of sandpaper. I'd like to make it smoother, particularly for the side walls.

How do I do that?

I was thinking about some sort of epoxy. Like, for example, epoxy-based garage floor stuff. I haven't gotten it, because I want to be sure that whatever I finish it with, it's -- you know -- safe to soak in. Not sure that an epoxy would ever achieve that.

How to get concrete really smooth --?

See vid. So apparently if you collect the most powdery bit of cement and make concrete with pure cement, i.e. no sand or anything, you can get a mirror-like finish. It's a lot of work but worth the effort, i think.

Put a layer of smooth plastic sheet against your wet concrete and leave it there until concrete has set. It will be as smooth as the surface of the plastic.