Many classes of applications exhibit significant tolerance to inaccuracies in their computations. Some examples include image processing, multimedia applications, and machine learning. These inaccuracies can be exploited to build circuits with smaller area, lower power, and higher performance. Most previous work restricts the approximate optimizations to a particular level of abstraction or step within the VLSI process. This paper shows that a combined multilevel approach is far more superior. Thus, this paper exploits different optimizations visible only at each particular level, leading to better results than single-level methods. Moreover, approximate computing is highly data-dependent. Therefore, in this paper, we study the stability of the approximate circuits when the circuit is optimized for a particular data distribution and the final workload differs from it. Previous work mainly considers a single input data distribution and that this distribution is equal to the final workload. Results show that our proposed method can find better and more optimal configurations compared with previous work and can achieve circuits, which are more robust in environments with dynamic workloads.