code: def _expm_multiply_simple_core(
      A, B, t, mu, m_star, s, tol=None, balance=False
  ):
      """
      A helper function.
      """
      if balance:
          raise NotImplementedError
      if tol is None:
          u_d = 2**-53
          tol = u_d
      F = B
      eta = np.exp(t * mu / float(s))
      for i in range(s):
          c1 = _exact_inf_norm(B)
          for j in range(m_star):
              coeff = t / float(s * (j + 1))
              B = coeff * A.dot(B)
              c2 = _exact_inf_norm(B)
              F = F + B
              if c1 + c2 <= tol * _exact_inf_norm(F):
                  break
              c1 = c2
          F = eta * F
          B = F
      return F
  
imports: from warnings import warn
  import numpy
  import scipy.linalg
  import scipy.sparse.linalg
  from scipy.linalg._decomp_qr import qr
  from scipy.sparse._sputils import is_pydata_spmatrix
  from scipy.sparse.linalg import aslinearoperator
  from scipy.sparse.linalg._interface import IdentityOperator
  from scipy.sparse.linalg._onenormest import onenormest
label_desc: Use image node_id 8 for calling a global function with example usage: _expm_multiply_simple_core(A, B, t, mu, m_star, s, tol, balance) and returns: F