def std_agg(cnt, s1, s2): return math.sqrt((s2/cnt) - (s1/cnt)**2)
 
 def find_better_split(self, var_idx):
        x, y = self.x.values[self.idxs,var_idx], self.y[self.idxs]
        sort_idx = np.argsort(x)
        sort_y,sort_x = y[sort_idx], x[sort_idx]
        rhs_cnt,rhs_sum,rhs_sum2 = self.n, sort_y.sum(), (sort_y**2).sum()
        lhs_cnt,lhs_sum,lhs_sum2 = 0,0.,0.

        for i in range(0,self.n-self.min_leaf-1):
            xi,yi = sort_x[i],sort_y[i]
            lhs_cnt += 1; rhs_cnt -= 1
            lhs_sum += yi; rhs_sum -= yi
            lhs_sum2 += yi**2; rhs_sum2 -= yi**2
            if i<self.min_leaf or xi==sort_x[i+1]:
                continue

            lhs_std = std_agg(lhs_cnt, lhs_sum, lhs_sum2)
            rhs_std = std_agg(rhs_cnt, rhs_sum, rhs_sum2)
            curr_score = lhs_std*lhs_cnt + rhs_std*rhs_cnt
            if curr_score<self.score: 
                self.var_idx,self.score,self.split = var_idx,curr_score,xi