Fortunately, the clean-up sweeps can be optimized with the mixed-precision approach, which lead to our fine-grained level method. To maintain the double-precision accuracy, the MPS data, the MPO data, the ENV data and the related operations, including the SVD decomposition and the update of the ENV, should stay in double precision. But the diagonalization procedure can be transformed into the mixed-precision while still remain the double-precision accuracy. In fact, in the DMRG sweep, the diagonalization procedure consumed around 60%-90% of the total computational time, making it the most time-consuming step in the DMRG sweep. Therefore, this mixed-precision transformation of the diagonalization procedure can obtain a satisfying performance speed-up in double-precision sweeps, and maintain the double-precision accuracy.