For navigating massive trees of floating point math, how does rust compare to c++

I have an algorithm planned out that stores massive trees that contain floating point data and requires very fast lookup, I was going to implement it in C++ but the perks of rust is making me re-think my decision.

For people that have experience with these data types with c++ and rust, how does the performance differ between the 2 languages. Compilation time does not matter to me, only runtime performance.