well understood that the symmetry energy from bulk matter is the difference between the energy of pure neutron matter and pure symmetric matter. Mathematically, it can we written as $$E_{Sym}(\rho,\delta)~=~E(\rho,\delta=1)-E(\rho,\delta=0),$$ where $\delta=\frac{\rho_n-\rho_p}{\rho_n+\rho_p}$ and $\rho=\rho_n+\rho_p$. $\rho_n$, $\rho_p$, and $\rho$ are the neutron, proton, and nuclear matter densities, respectively. The symmetry energy has great importance in the dense matter existing in the neutron stars, but only indirect information can be extracted from astrophysical observations [@Latt04]. It is also important in the quark gluon plasma (QGP) and hadron gas (HG) phase [@Toro11]. The QGP and HG phases existed in the early stage of the evolution of Universe (about 15 billion years ago) and are inaccessible nowadays. It is difficult to recreate these conditions, although numerous experiments are occurring at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) [@Nagl11]. Heavy-ion reactions, during which matter goes through compression and expansion, are considered to be the true testing ground for the hot and dense matter phases. The nuclear equation of state (NEOS) and the density dependence of the symmetry energy can be probed by some observables in intermediate-energy heavy-ion collisions (HICs). The softness of the NEOS has been well described in the 