code: def log_prob_normal_in(a: Tensor, b: Tensor) -> Tensor:
      r"""Computes the probability that a standard normal random variable takes a value
      in \[a, b\], i.e. log(Phi(b) - Phi(a)), where Phi is the standard normal CDF.
      Returns accurate values and permits numerically stable backward passes for inputs
      in [-1e100, 1e100] for double precision and [-1e20, 1e20] for single precision.
      In contrast, a naive approach is not numerically accurate beyond [-10, 10].
  
      Args:
          a: Tensor of lower integration bounds of the Gaussian probability measure.
          b: Tensor of upper integration bounds of the Gaussian probability measure.
  
      Returns:
          Tensor of the log probabilities.
      """
      if not (a < b).all():
          raise ValueError(
              "Received input tensors a, b for which not all a < b."
          )
      # if abs(b) > abs(a), we use Phi(b) - Phi(a) = Phi(-a) - Phi(-b), since the
      # right tail converges to 0 from below, leading to digit cancellation issues, while
      # the left tail of log_ndtr is well behaved and results in large negative numbers
      rev_cond = b.abs() > a.abs()  # condition for reversal of inputs
      if rev_cond.any():
          c = torch.where(rev_cond, -b, a)
          b = torch.where(rev_cond, -a, b)
          a = c  # after we updated b, can assign c to a
      return logdiffexp(log_a=log_ndtr(a), log_b=log_ndtr(b))
  
imports: from __future__ import annotations
  import math
  from functools import lru_cache
  from math import pi
  from numbers import Number
  from typing import Any, Callable, Iterable, Iterator, Optional, Tuple, Union
  import torch
  from botorch.utils.safe_math import logdiffexp
  from numpy.polynomial.legendre import leggauss
  from torch import BoolTensor, LongTensor, Tensor
label_desc: Use image node_id 14 for calling a global function with example usage: log_prob_normal_in(a, b) and returns: logdiffexp