Which is faster?

This is too simplistic example to give any meaningful answer. What’s Type? What’s value? If it’s i32 and 42 than they both compile to the exact same thing. But if Type is Drop than the second will call the destructor on each iteration. (I’ve also written previously about similar example with BorrowedBuf¹).

Side note, don't fall into the trap of premature optimization. You'll more than likely end up shooting yourself in the foot for something that usually doesn't matter in most cases.

Functionally equivalent, the compiler will optimize lots for you. As the programmer, your focus should be on whether that variable is relevant to the loop's scope exclusively or not (i.e. if you need to access the variable after the loop has modified it). If not, keep it in the loop so that its easier to read your code.

I would say that they are equivalent. If I'm not mistaken, let statements only reserves space on the stack, and this only increments the stack register.

And on the latter snippet, the compiler would certainly not bother to modify the stack pointer as the type doesn't change.

according to godbolt: https://rust.godbolt.org/z/hP5Y3qMPW

use rand::random;

pub fn main1() {
    let mut var : u128;
    loop {
        var = random();
    }
}

pub fn main2() {
    loop {
        let var : u128 = random();
    }
}

compiles to:

example::main1::h45edf333d7832d08:
.Lfunc_begin8:
        sub     rsp, 24
.LBB8_1:
.Ltmp80:
        mov     rax, qword ptr [rip + rand::random::he3c23ceb967a3e28@GOTPCREL]
        call    rax
        mov     qword ptr [rsp + 8], rdx
        mov     qword ptr [rsp], rax
        jmp     .LBB8_1
.Ltmp81:
.Lfunc_end8:

example::main2::h1a899b25b96d66db:
.Lfunc_begin9:
        sub     rsp, 24
.LBB9_1:
.Ltmp82:
        mov     rax, qword ptr [rip + rand::random::he3c23ceb967a3e28@GOTPCREL]
        call    rax
        mov     qword ptr [rsp + 8], rdx
        mov     qword ptr [rsp], rax
        jmp     .LBB9_1
.Ltmp83:
.Lfunc_end9:
        jmp     .LBB9_1

So yeah, exactly the same thing.

Fascinating! Thank you for sharing this.

let statements only reserves space on the stack

It is not guaranteed to do that. It could also use a register or be optimized out completly (like in the example you posted in the other comment).

The stack pointer is also not changed for each local variable, but instead for each function call, so it wouldn't make a difference anyway.
- Ok! Thanks for the clarification !

The second one is more expensive as you constantly are creating a new variable. In the first one you just constantly change the value of a variable.

This is Rust not Python

They're both optimised out by the compiler. If you disable compiler optimisations, they're identical in machine code anyway, unless you introduce a second loop, in which case the first will be more memory efficient as the memory used in the first loop can be reused in the second loop, whereas if you declare the variable outside the loop it can't (again, without compiler optimisations, which make the whole comparison pointless).
This is just flat out false.
That's what I thought.