code: def interp_fit_dopri(y0, y1, k, dt):
      # Fit a polynomial to the results of a Runge-Kutta step.
      dps_c_mid = jnp.array(
          [
              6025192743 / 30085553152 / 2,
              0,
              51252292925 / 65400821598 / 2,
              -2691868925 / 45128329728 / 2,
              187940372067 / 1594534317056 / 2,
              -1776094331 / 19743644256 / 2,
              11237099 / 235043384 / 2,
          ],
          dtype=y0.dtype,
      )
      y_mid = y0 + dt.astype(y0.dtype) * jnp.dot(dps_c_mid, k)
      return jnp.asarray(
          fit_4th_order_polynomial(y0, y1, y_mid, k[0], k[-1], dt)
      )
  
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 3 for calling a global function with example usage: interp_fit_dopri(y0, y1, k, dt) and returns: jnp