Kohn-Sham density functional theory (KS-DFT) has been the most popular computational quantum mechanical modeling method since the last century. At the center of KS-DFT, designing better exchange-correlation (XC) functionals gains the most attention. In this work, we explored two different exchange-correlation functional approximations: the Fermi-Amaldi (FA) mixed functional and the simplified nonlocal XC density approximation (SNXCDA). The FA functional was first proposed by Fermi to eliminate the non-physical self-interaction among electrons. We proposed linear combinations of Fermi-Amaldi functional with SVWN5 functional and BLYP functional accordingly. The unknown coefficients in the combinations were determined through the linear regression technique. The final result shows that Fermi-Amaldi energy has little impact on exchange-correlation energy, and should not be considered as a good correction for improving the performance of other exchange-correlation functionals. The design of SNXCDA was inspired by the success of simplified nonlocal density approximation in kinetic energy functional. The unknown kernel of SNXCDA was determined by enforcing the correct linear response at the limit of uniform electron gas (UEG). However, the simulation results show that SNXCDA violates the sum rule severely. Thus SNXCDA should not be considered as a good approximation.