  Approximate circuits trading the power consumption for the quality of results
play a key role in the development of energy-aware systems. Designing complex
approximate circuits is, however, a very difficult and computationally
demanding process. When deploying approximate circuits, various error metrics
(e.g., mean average error, worst-case error, error rate), as well as other
constraints (e.g., correct multiplication by 0), have to be considered. The
state-of-the-art approximation methods typically focus on a single metric which
significantly limits the applicability of the resulting circuits. In this
paper, we experimentally investigate how various error metrics and their
combinations affect the reduction of the power consumption that can be
achieved. To this end, we extend evolutionary-driven techniques that allow us
to effectively explore the design space of the approximate circuits. We
identify principal limitations when complex error constraints are required as
well as important correlations among the error metrics enabling the
construction of circuits providing the best-known trade-offs between the power
reduction and combined error constraints.
