code: def fatmaximum(
      a: Tensor,
      b: Tensor,
      tau: Union[float, Tensor] = TAU,
      alpha: float = ALPHA,
  ) -> Tensor:
      """Computes a smooth approximation to torch.maximum(a, b) with a fat tail.
  
      Args:
          a: The first Tensor from which to compute the smoothed component-wise maximum.
          b: The second Tensor from which to compute the smoothed component-wise maximum.
          tau: Temperature parameter controlling the smoothness of the approximation. A
              smaller tau corresponds to a tighter approximation that leads to a sharper
              objective landscape that might be more difficult to optimize.
  
      Returns:
          A smooth approximation of torch.maximum(a, b).
      """
      return fatmax(
          torch.stack(torch.broadcast_tensors(a, b), dim=-1),
          dim=-1,
          keepdim=False,
          tau=tau,
      )
  
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 24 for calling a global function with example usage: fatmaximum(a, b, tau, alpha) and returns: fatmax