One standard method to measure relative error in price predictions is to compute the discrepancy using the logarithm of the estimates. This mathematically translates to the Logarithmic Root Mean Squared Error (Log RMSE), which measures the root-mean-squared-error between the logarithm of the predicted price $\hat{y}_i$ and the logarithm of the actual label price $y_i$. The formal equation for a dataset of size $n$ is: $\sqrt{\frac{1}{n}\sum_{i=1}^n\left(\log y_i -\log \hat{y}_i\right)^2}$. This metric is highly effective because a small discrepancy $\delta$ where $|\log y - \log \hat{y}| \leq \delta$ directly translates into the relative ratio $e^{-\delta} \leq \frac{\hat{y}}{y} \leq e^\delta$.