We performed a Pareto analysis (described further in section 1.2 of the SI) and found that we cannot entirely eliminate the errors in the pressure derivative properties and temperature derivative properties simultaneously. Specifically, we lose accuracy in pressure derivative properties, such as density, if we push the MSE in temperature derivatives properties too low. Similarly, errors in MSE in the temperature derivative properties, heat capacity, significantly increase when we try to push the MSE in pressure derivative properties to a minimum. However, we found that the pressure derivative properties do not suffer as much from the assumptions in the rigid water model or in MD simulations as do the temperature properties. Thus, we searched for the minimum MSE in C P,res which permitted the MSE in V res or density to be as small as experimental uncertainty i. e. uncertainty in density estimated using IAPWS95 EOS. This uncertainty of the experimental liquid phase density estimated using IAPWS95 ranges from ± 0.001% to ± 0.02%. In particular, the error in experimental density estimates at atmospheric pressure is extremely small, on the order of ≤ 0.0001%. Classical molecular simulations are unlikely to achieve a level of accuracy of 0.0001% as they omit both electronic and nuclear quantum effects. Additionally, such error would require orders of magnitude more simulations to reach this level of statistical accuracy which is not practical or useful given the levels of precision for most experiments simulations are compared to. We therefore search for a global minimum in mean square error of density (MSE) by setting a very low target, arbitrarily at 10 -6 . However, we do allow a certain MSE of C P,res , with a value obtained below, that allows us to achive MSE in V res within ±0.02% of experimental uncertainty.