code: def _interp_fit(y0, y1, y_mid, f0, f1, dt):
      """Fit coefficients for 4th order polynomial interpolation.
  
      Args:
          y0: function value at the start of the interval.
          y1: function value at the end of the interval.
          y_mid: function value at the mid-point of the interval.
          f0: derivative value at the start of the interval.
          f1: derivative value at the end of the interval.
          dt: width of the interval.
  
      Returns:
          List of coefficients `[a, b, c, d, e]` for interpolating with the polynomial
          `p = a * x ** 4 + b * x ** 3 + c * x ** 2 + d * x + e` for values of `x`
          between 0 (start of interval) and 1 (end of interval).
      """
      a = 2 * dt * (f1 - f0) - 8 * (y1 + y0) + 16 * y_mid
      b = dt * (5 * f0 - 3 * f1) + 18 * y0 + 14 * y1 - 32 * y_mid
      c = dt * (f1 - 4 * f0) - 11 * y0 - 5 * y1 + 16 * y_mid
      d = dt * f0
      e = y0
      return [e, d, c, b, a]
  
label_desc: Use image node_id 1 for calling a global function with example usage: _interp_fit(y0, y1, y_mid, f0, f1, dt) and returns: list