code: def rk4_alt_step_func(func, t0, dt, t1, y0, f0=None, perturb=False):
      """Smaller error with slightly more compute."""
      k1 = f0
      if k1 is None:
          k1 = func(
              t0, y0, perturb=Perturb.NEXT if perturb else Perturb.NONE
          )
      k2 = func(t0 + dt * _one_third, y0 + dt * k1 * _one_third)
      k3 = func(t0 + dt * _two_thirds, y0 + dt * (k2 - k1 * _one_third))
      k4 = func(
          t1,
          y0 + dt * (k1 - k2 + k3),
          perturb=Perturb.PREV if perturb else Perturb.NONE,
      )
      return (k1 + 3 * (k2 + k3) + k4) * dt * 0.125
  
imports: import bisect
  import collections
  import torch
  from .event_handling import find_event
  from .interp import _interp_evaluate, _interp_fit
  from .misc import _compute_error_ratio, _select_initial_step, _optimal_step_size
  from .misc import Perturb
  from .solvers import AdaptiveStepsizeEventODESolver
label_desc: Use image node_id 3 for calling a global function with example usage: rk4_alt_step_func(func, t0, dt, t1, y0, f0, perturb) and returns: unknown