def METHOD_NAME(fitter, model, fake_toas):
    t = fake_toas
    delta_f = (1 / (t.last_MJD - t.first_MJD)).to(u.Hz)
    # Unchanged model, fitting should be trivial
    f_0 = fitter(t, model, track_mode="use_pulse_numbers")
    f_0.fit_toas()
    assert abs(f_0.model.F0.quantity - model.F0.quantity) < 0.01 * delta_f
    m_2 = deepcopy(model)
    m_2.F0.quantity += 2 * delta_f
    m_2.free_params = ["F0"]
    # Check fitter with and without tracking
    with pytest.raises(ValueError):
        fitter(t, m_2, track_mode="capybara")
    f_1 = fitter(t, m_2, track_mode="nearest")
    with contextlib.suppress(ValueError):
        f_1.fit_toas()
        assert abs(f_1.model.F0.quantity - model.F0.quantity) > 0.1 * delta_f
    f_2 = fitter(t, m_2, track_mode="use_pulse_numbers")
    f_2.fit_toas()
    assert abs(f_2.model.F0.quantity - model.F0.quantity) < 0.01 * delta_f