Q: Does the compiler optimize math expressions? Does rustc optimize such expressions?

*

*2*x -> x<<1

*x/2 -> x>>1

*x % 8 -> x&7

*and such


A: Such trivial optimizations are in the domain of LLVM optimization passes, in fact generated assembly is even better and more correct.
2*x is compiled to single instruction lea rax, [rdi + rdi], which on all modern x86 processors is single uop (relevant question)
x/2 for signed numbers is compiled to fastest and the correct way, which gives right answer in case of -1 (relevant question
mov     rax, rdi
shr     rax, 63
add     rax, rdi 
sar     rax 

but compiles to right shift for unsigned numbers
mov     rax, rdi
shr     rax

same story goes for x % 8 it compiles to long assembly for signed numbers (for negative cases)
mov     rax, rdi
lea     rcx, [rdi + 7]
test    rdi, rdi
cmovns  rcx, rdi
and     rcx, -8
sub     rax, rcx
ret

and to and instruction for unsigned numbers (relevant question)
 mov     rax, rdi
 and     eax, 7
 ret

Godbolt link
