The Rust runtime is larger than C's (I imagine it's not much larger than C++, but this is already way too large). AFAIK, nobody ever proved it works as designed. The fact that it's design is not very stable is also a problem.
Now, with some more thought about it, C itself is not a great target for correctness proofs. Too much is left unspecified, and there is little agreement over some of the lower level stuff. A simplified version of Rust might be a better target than C, if somebody ever creates it, but a lot of the safety would have to be left out of it.
Rust also lets you write a custom runtime by specifying a start function if you want.
> The fact that it's design is not very stable is also a problem.
Rust is stable.
I believe that it is smaller than C++'s but larger than C's, but I'm not a mega expert here. I used to know where those files were located in-tree, but don't anymore.
I think there's also several distinctions you can draw here; for example, strictly speaking, almost no runtime is required, but if you're using say, the standard library, you still might end up with a bunch of code. The actual requirements are very small though.
> AFAIK, nobody ever proved it works as designed. The fact that it's design is not very stable is also a problem.
Sorry, I don't understand what you mean here. The runtime?
> A simplified version of Rust might be a better target than C, if somebody ever creates it, but a lot of the safety would have to be left out of it.
I _think_ with the above comments, you mean the Rust langauge overall, not the runtime, right? So, Rust _is_ very stable; post 1.0 we have made extremely small breaking changes, corresponding to the way new C++ standards sometimes introduce minor technical backwards incompatibilities. As for correctness proofs, there are multiple academic institutions working on it; and they don't have to "leave the safety out"; that's what they're trying to prove!
Finally, we link to jemalloc, which is an additional bit of runtime of its own (which can be turned off with alloc_system)
There's also compiler-rt which does some of the eh stuff for panics and whatnot.
Many people say "no runtime" to mean "small runtime like C or C++ have" rather than literally no runtime. This is due to the confusion around interpreters sometimes being called "runtimes."