def METHOD_NAME(factorize_task, already_factorized):
    """More optimization iters should yield nonincreasing error."""
    prev_nmse = np.inf
    for n_iters in [0, 1, 2, 4]:
        factorize_task.n_iters = n_iters
        maybe_nmse = _check_factorization(factorize_task, prev_nmse, already_factorized=already_factorized)
        prev_nmse = maybe_nmse if maybe_nmse else prev_nmse