But the first several sweeps are set to run with a relatively small bond dimension, and will increase sweep by sweep. At this circumstance, the conversion process in the mixed-precision diagonalization method will consume much more time than other operations. resulting in a deceleration of overall performance. This is why the overall speed-up of the mixed-precision method is not as good as the speed-up of a single sweep. Hence, the mixed-precision scheme, combining both of these two level mixed-precision methods, can achieve the best performance of these three mixed-precision settings, and also maintain the double-precision accuracy. As for the the active space size aspect, the speed-up will firstly increase with the growth of the active space size, and then decrease. At the beginning, with a relatively small space, the total computational time is short. Therefore there is no much different of the total computational time between the double-precision method and the mixed-precision scheme, even though the performance of one single sweep is increased. Thus, with the growth of the system, the speed-up, both in total computational time and in a single sweep, will increase significantly. After reaching the maximum point, around 28-40 active orbitals for different system, the speed-up will slightly decrease. There are several reasons for this decrease of performance. The first and foremost reason is the performance of the matrix product operations, which depends on the implementation of the MKL library, that is slightly reduced with the growth of the matrix size when the size is large enough. The second reason is when the system is too big, the total amount of data would be larger than the memory of our computing node. Therefore, one must store the unused ENVs on the disk, when we doing the sweep, and load the corresponding ENV back to memory when it is required. This memory store and load operations delays the overall performance, as the data is stored in text form instead of binary form. Another reason is that, with the growth of the system, the ratio of computational cost for the ENV update operation will grow. But this operation is not optimized in the fine-grained level method, causing a slight reduction of the performance.