code: def cauchy(x: Tensor) -> Tensor:
      """Computes a Lorentzian, i.e. an un-normalized Cauchy density function."""
      return 1 / (1 + x.square())
  
imports: from __future__ import annotations
  import math
  from typing import Callable, Tuple, Union
  import torch
  from botorch.exceptions import UnsupportedError
  from botorch.utils.constants import get_constants_like
  from torch import finfo, Tensor
  from torch.nn.functional import softplus
label_desc: Use image node_id 28 for calling a global function with example usage: cauchy(x) and returns: unknown