Efficient way to implement Towers of Hanoi with steps returned as string - go

Question

I'm comparing several algorithms in JS, Rust and Go. I implemented Towsers of Hanoi this way in Go:
func Hanoi() (hanoi func(n int, from, via, to string) string) {
var moves strings.Builder
var hanoiRe func(n int, from, via, to string)
hanoiRe = func(n int, from, via, to string) {
if n > 0 {
hanoiRe(n-1, from, to, via)
moves.WriteString(from)
moves.WriteString("->")
moves.WriteString(to)
moves.WriteString("\n")
hanoiRe(n-1, via, from, to)
}
}
hanoi = func(n int, from, via, to string) string {
hanoiRe(n, from, via, to)
return moves.String()
}
return
}
But this implementation is much slower than JS or Rust. So I think, this could be done faster. But how?
I already tried type hanoi struct{moves strings.Builder} with func (h *hanoi) ..., which is a bit slower. The way using a string and moves += ...is much slower.
EDIT:
My comparisons:
JS:
class HanoiJS {
constructor() {
this.moves = "";
}
hanoi(n, from, via, to) {
if (n > 0) {
this.hanoi(n - 1, from, to, via);
this.moves += from + "->" + to + "\n";
this.hanoi(n - 1, via, from, to);
}
return this.moves;
}
}
Rust:
pub struct Hanoi {
moves: String
}
impl Hanoi {
pub fn new() -> Hanoi {
Hanoi {
moves: String::new()
}
}
pub fn hanoi(&mut self, n: i32, from: &str, via: &str, to: &str) -> &str {
if n > 0 {
self.hanoi(n - 1, from, to, via);
self.moves.push_str(from);
self.moves.push_str("->");
self.moves.push_str(to);
self.moves.push_str("\n");
self.hanoi(n - 1, via, from, to);
}
return &self.moves;
}
}
Compared with n=20 and 5 times: