Are we in a simulation?

One of the old philosophical problems, also tackled by movies like Matrix, along with many others, is, simply: Are we living inside a simulation?

Without going into philosophical aspects of that, I've got to say that if we are, it is damn impressive simulation indeed.

Take issue of observable universe, for example. Let's for starters assume that the rules of the universe must be fixed and running from the beginning and whoever is running can't just improvise general rules at some point. I make this assumption since as far as we've perceived so far, the rules have not changed - system (in our solar system level) has been the same from the start, introducing us such weird things as epicycles when we got it wrong.

But this is just small potatoes so far. Let's expand this a bit. Our galaxy, Milkyway, has estimated of 100-400 billion stars (so, 100*10^9 - 400*10^9, in a bit more easily readable notation when talking about huge scales), and by now we can assume that quite many, if not most of these stars have at least one, if not more, planets. So we're talking at least trillion (1*10^12) major objects, and we're completely ignoring things as asteroid belts and such.

And expanding this again. Ultra Deep Field shows just tiny, tiny fraction of sky we see (way smaller area than the moon!) and it alone shows something like 10000 galaxies. Expand this to entire sky and we're talking about hundreds of billions of galaxies (100*10^9) again. Each with trillion (1*10^12) major objects. Which would place total number of major objects to somewhere around 1*10^23 range. That's 1, with 23 zeros following.

It's late when I'm writing this so there might be some stupid math errors, but nevertheless, I don't think I'm too far off. And again, we're still discussing only planet- or moon-sized objects and larger; smaller objects are so far ignored.

So again, returning to assumption that the simulation must be mathematically perfect from the start, it would have to consider gravity interaction of all these objects, all the time.

And here we are, where we can't even analyze such problems with mere 3 objects (three-body problem) but only in some very limited scenarios!

So I say again, if this a simulation, it must be backed by some pretty impressive mathematics to be able to simulate all these objects, since we certainly don't have capabilities for even infinitely tiny fraction of something like it. Without cheating, of course, but such cheat would be kinda obvious later with sudden changes in system behavior when exposed to detailed observation...

Of course system might be limited to things we can observe, but this was kinda my point with this - at the moment we can observe stupidly huge amount of objects - not necessarily directly, nor all the time, but still the behavior of objects previously observed must remain consistent during the simulation, in case we are to observe them again later. So even with cheats, things get pretty heavy.

I know, there are arguments to counter things I've said here, but nevertheless the energy cost for running such simulation would be simply enormous. Even if the rules if this universe don't apply in universe that is running the simulation.