Equations of state (EoS) are a fundamental subject in high pressure/temperature (PT) research. Ab initio calculations based on density functional theory (DFT) can provide valuable information about a material's EoS at PT conditions that cannot be easily accessed experimentally. However, these calculations have systematic errors due to (1) a lack of a precise description of the exchange correlation energy, (2) methodological limitations in the way temperature is addressed, for instance, anharmonicity at high temperatures in quasiharmonic calculations. To address the first issue, we have improved, developed, and tested correction schemes aiming to remove DFT errors and to produce predictive low temperature EoS with accuracy comparable to experiments. We have investigated four schemes and applied them to three different functionals. The second issue has been addressed with a simple anharmonic correction that effectively removed high temperature anharmonic errors.