A data processing system and method for regulating a voltage supply to functional circuitry configured to operate from a variable voltage supply, the functional circuitry having at least one error correction circuit configured to detect and repair errors in operation of the functional circuitry. Voltage regulator circuitry provides the voltage supply to the functional circuitry, and modifies the voltage level of the voltage supply based on a feedback control signal. Error rate history circuitry receives error indications from the error correction circuit during operation of the functional circuitry and generates error rate history information therefrom. An adaptive controller then generates the feedback control signal in dependence on the error rate history information such that the adaptive controller adjusts the feedback control signal over time having regard to the error rate history information in order to obtain a predetermined target non-zero error rate within the functional circuitry.