code: def gelu(x: ArrayLike, approximate: bool = True) -> Array:
      r"""Gaussian error linear unit activation function.
  
      If ``approximate=False``, computes the element-wise function:
  
      .. math::
        \mathrm{gelu}(x) = \frac{x}{2} \left(1 + \mathrm{erf} \left(
          \frac{x}{\sqrt{2}} \right) \right)
  
      If ``approximate=True``, uses the approximate formulation of GELU:
  
      .. math::
        \mathrm{gelu}(x) = \frac{x}{2} \left(1 + \mathrm{tanh} \left(
          \sqrt{\frac{2}{\pi}} \left(x + 0.044715 x^3 \right) \right) \right)
  
      For more information, see `Gaussian Error Linear Units (GELUs)
      <https://arxiv.org/abs/1606.08415>`_, section 2.
  
      Args:
        x : input array
        approximate: whether to use the approximate or exact formulation.
      """
      [x_arr] = numpy_util.promote_args_inexact("gelu", x)
  
      if approximate:
          sqrt_2_over_pi = np.sqrt(2 / np.pi).astype(x_arr.dtype)
          cdf = 0.5 * (
              1.0
              + jnp.tanh(
                  sqrt_2_over_pi * (x_arr + 0.044715 * (x_arr**3))
              )
          )
          return x_arr * cdf
      else:
          sqrt_2 = np.sqrt(2).astype(x_arr.dtype)
          return jnp.array(
              x_arr * (lax.erf(x_arr / sqrt_2) + 1) / 2,
              dtype=x_arr.dtype,
          )
  
imports: from __future__ import annotations
  from functools import partial
  import operator
  import numpy
  from typing import Any
  import jax
  import jax.numpy
  from jax import custom_jvp
  from jax import lax
  from jax._src import config
  from jax._src import core
  from jax._src import dtypes
  from jax._src import util
  from jax._src.core import AxisName
  from jax._src.numpy import util
  from jax._src.typing import Array, ArrayLike
  from jax._src.ops.special import logsumexp
label_desc: Use image node_id 13 for calling a global function with example usage: gelu(x, approximate) and returns: unknown, jnp