code: def fit_4th_order_polynomial(y0, y1, y_mid, dy0, dy1, dt):
      dt = dt.astype(y0.dtype)
      a = (
          -2.0 * dt * dy0
          + 2.0 * dt * dy1
          - 8.0 * y0
          - 8.0 * y1
          + 16.0 * y_mid
      )
      b = (
          5.0 * dt * dy0
          - 3.0 * dt * dy1
          + 18.0 * y0
          + 14.0 * y1
          - 32.0 * y_mid
      )
      c = (
          -4.0 * dt * dy0
          + dt * dy1
          - 11.0 * y0
          - 5.0 * y1
          + 16.0 * y_mid
      )
      d = dt * dy0
      e = y0
      return a, b, c, d, e
  
imports: from functools import partial
  import operator
  import jax
  import jax.numpy
  from jax._src import core
  from jax import custom_derivatives
  from jax import lax
  from jax._src.numpy.util import promote_dtypes_inexact
  from jax._src.util import safe_map, safe_zip
  from jax.flatten_util import ravel_pytree
  from jax.tree_util import tree_leaves, tree_map
  from jax._src import linear_util
label_desc: Use image node_id 4 for calling a global function with example usage: fit_4th_order_polynomial(y0, y1, y_mid, dy0, dy1, dt) and returns: a,  b,  c,  d,  e