Measure and improve the constant numbers used when building the tree

[Clément Renault]

We must take three parameters into account:

1. Time to build the tree
2. Relevancy of the searches
3. Time to search in the tree

Fun fact: the lowest in the tree you are, the less impact a dummy plane has on the search cost.

---

arroy/src/writer.rs

Lines 248 to 259 in 7fc6031

     if split_imbalance(children_left.len(), children_right.len()) < 0.95 
         || remaining_attempts == 0 
     { 
         break normal; 
     } 
  
     remaining_attempts -= 1; 
 }; 
  
 // If we didn't find a hyperplane, just randomize sides as a last option 
 // and set the split plane to zero as a dummy plane. 
 while split_imbalance(children_left.len(), children_right.len()) > 0.99 { 

fn split_imbalance(left_indices_len: usize, right_indices_len: usize) -> f64 {
    let ls = left_indices_len as f64;
    let rs = right_indices_len as f64;
    let f = ls / (ls + rs + f64::EPSILON); // Avoid 0/0
    f.max(1.0 - f)
}

fn main() {
    dbg!(split_imbalance(29464, 18394));
    dbg!(split_imbalance(30000, 30000));
    dbg!(split_imbalance(30000, 1580));
}