code: def _HalfCauchy_logprob(self, value):
      if self._validate_args:
          self._validate_sample(value)
      value = torch.as_tensor(
          value,
          dtype=self.base_dist.scale.dtype,
          device=self.base_dist.scale.device,
      )
      log_prob = self.base_dist.log_prob(value) + math.log(2)
      log_prob.masked_fill_(
          value.expand(log_prob.shape) < 0, -float("inf")
      )
      return log_prob
  
file_path: pyro/pyro/distributions/torch_patch.py
imports: import functools
  import math
  import warnings
  import weakref
  import torch
label_desc: Use image node_id 5 for calling a global function with example usage: _HalfCauchy_logprob(value) and returns: log_prob