code: def _log_ndtr_single(a: float) -> float:
      if a > 6:
          return -_ndtr_single(-a)
      if a > -20:
          return math.log(_ndtr_single(a))
  
      log_LHS = (
          -0.5 * a**2 - math.log(-a) - 0.5 * math.log(2 * math.pi)
      )
      last_total = 0.0
      right_hand_side = 1.0
      numerator = 1.0
      denom_factor = 1.0
      denom_cons = 1 / a**2
      sign = 1
      i = 0
  
      while abs(last_total - right_hand_side) > sys.float_info.epsilon:
          i += 1
          last_total = right_hand_side
          sign = -sign
          denom_factor *= denom_cons
          numerator *= 2 * i - 1
          right_hand_side += sign * numerator * denom_factor
  
      return log_LHS + math.log(right_hand_side)
  
imports: import functools
  import math
  import sys
  from typing import Callable
  from typing import Optional
  from typing import Union
  import numpy
  from optuna.samplers._tpe._erf import erf
label_desc: Use image node_id 5 for calling a global function with example usage: _log_ndtr_single(a) and returns: unknown, unknown, math