code: def _build_subtree(self, left, depth, epsilon):
      if depth == 0:
          return self._single_step(left, epsilon)
  
      tree1, diverging, turning = self._build_subtree(
          left, depth - 1, epsilon
      )
      if diverging or turning:
          return tree1, diverging, turning
  
      tree2, diverging, turning = self._build_subtree(
          tree1.right, depth - 1, epsilon
      )
  
      left, right = tree1.left, tree2.right
  
      if not (diverging or turning):
          p_sum = tree1.p_sum + tree2.p_sum
          turning = (p_sum.dot(left.v) <= 0) or (
              p_sum.dot(right.v) <= 0
          )
          # Additional U turn check only when depth > 1 to avoid redundant work.
          if depth - 1 > 0:
              p_sum1 = tree1.p_sum + tree2.left.p.data
              turning1 = (p_sum1.dot(tree1.left.v) <= 0) or (
                  p_sum1.dot(tree2.left.v) <= 0
              )
              p_sum2 = tree1.right.p.data + tree2.p_sum
              turning2 = (p_sum2.dot(tree1.right.v) <= 0) or (
                  p_sum2.dot(tree2.right.v) <= 0
              )
              turning = turning | turning1 | turning2
  
          log_size = np.logaddexp(tree1.log_size, tree2.log_size)
          if logbern(tree2.log_size - log_size):
              proposal = tree2.proposal
          else:
              proposal = tree1.proposal
      else:
          p_sum = tree1.p_sum
          log_size = tree1.log_size
          proposal = tree1.proposal
  
      tree = Subtree(left, right, p_sum, proposal, log_size)
      return tree, diverging, turning
  
imports: from __future__ import annotations
  from collections import namedtuple
  import numpy
  from pymc.math import logbern
  from pymc.pytensorf import floatX
  from pymc.stats.convergence import SamplerWarning
  from pymc.step_methods.compound import Competence
  from pymc.step_methods.hmc import integration
  from pymc.step_methods.hmc.base_hmc import BaseHMC, DivergenceInfo, HMCStepData
  from pymc.step_methods.hmc.integration import IntegrationError, State
  from pymc.vartypes import continuous_types
label_desc: Use image node_id 4 for calling the _Tree obj's underlying member method code with example usage: obj._build_subtree(left, depth, epsilon) and returns: tree,  diverging,  turning, self, tree1,  diverging,  turning