code: def log_softplus(
      x: Tensor, tau: Union[float, Tensor] = TAU
  ) -> Tensor:
      """Computes the logarithm of the softplus function with high numerical accuracy.
  
      Args:
          x: Input tensor, should have single or double precision floats.
          tau: Decreasing tau increases the tightness of the
              approximation to ReLU. Non-negative and defaults to 1.0.
  
      Returns:
          Tensor corresponding to `log(softplus(x))`.
      """
      check_dtype_float32_or_float64(x)
      tau = torch.as_tensor(tau, dtype=x.dtype, device=x.device)
      # cutoff chosen to achieve accuracy to machine epsilon
      upper = 16 if x.dtype == torch.float32 else 32
      lower = -15 if x.dtype == torch.float32 else -35
      mask = x / tau > lower
      return torch.where(
          mask,
          softplus(
              x.masked_fill(~mask, lower),
              beta=(1 / tau),
              threshold=upper,
          ).log(),
          x / tau + tau.log(),
      )
  
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 16 for calling a global function with example usage: log_softplus(x, tau) and returns: torch