the soft ($\gamma_i$=0.5) and stiff ($\gamma_i$=1.5) symmetry energies, respectively, for the system $^{132}$Sn + $^{132}$Sn.](figure3.eps){width="90mm"}

To see the virtual change in the symmetry energy due to the change in the density, we display in Fig. \[fig:3\] the incident energy dependence of $(\rho/\rho_0)^{\gamma_i}$, which is proportional to the symmetry energy, at the time of the maximum compression (left panel) and at the freeze-out time (right panel). At the time of maximum compression, the symmetry energy rises with the increasing incident energy (increase in density). As the density is more than the normal nuclear matter density in this region, the stiff symmetry energy is stronger than the soft one. With increasing incident energy (increase in density), the stiff symmetry energy is changing drastically, while, the soft symmetry energy shows little change. This exactly coincided with the ideal picture of density dependence of the symmetry energy. On the other hand, if we look at the energy dependence of $(\rho/\rho_0)^{\gamma_i}$ at $t$ = 200 fm/c, the situation is totally different. The symmetry energy is found to decrease with increasing incident energy (decrease in density). Now the density is lower than the normal nuclear matter density, so the magnitude of the soft symmetry energy is 