Finally, in the specific case of formation energy calculation, error cancellation may cause additive errors to appear as proportional errors. Assume, for instance, that a particular reference state is off by an additive error. One would expect the same additive error to appear in a system very similar to the reference state. Therefore, when the formation energy is calculated by subtracting the reference energy from the energy of this near-reference-state system, the additive error will mostly cancel, leaving behind a small additive error. The near-reference system will also have a small-magnitude formation energy. In summary, small-magnitude formation energy systems would likely exhibit small additive errors due to a large degree of error cancellation. However, if we consider a material that has a large-magnitude formation energy, it must be dissimilar from the reference state in a meaningful way. Therefore, when we calculate the formation energy, we would expect less error cancellation between the additive error of the system and that of the reference state. In summary, large-magnitude formation energy systems would be expected to exhibit larger additive errors due to a lesser degree of error cancellation. Fur-thermore, we would expect DFT's additive errors cause either an overestimation or an underestimation of the formation energies, not just a random increase in the spread of the formation energies we move away from the reference state. In mathematical terms, this means we would expect a proportional error, not a proportional absolute error. Altogether, we would expect this error cancellation effect to cause additive errors to appear as proportional errors in the case of formation energies.