Density of observables from local derivatives

We derive a formula to calculate the local change to the log of any density of states for smooth real observables. Using this in Monte-Carlo simulations, we are able to calculate the expectation value of the observable with a precision often better than standard sampling. The method can be applied to previously generated configurations, as long as the analysis uses the same action used to generate the configurations. We show that for observables such as Wilson line correlators, errors are reduced by up to 4 times.