Current logic synthesis techniques are ineffective for arithmetic circuits. They perform poorly for XOR-dominated circuits, and those with a high fan-in dependency between inputs and outputs. Many optimizers, therefore employ libraries of hand-optimized arithmetic components, but cannot optimize across component boundaries. To remedy this situation, we introduce a new logic synthesis algorithm which analyzes the input circuit based on its behavior on a set of random assignments of input variables, and outputs a structural implementation of the input circuit. The method presented here is similar to the covering algorithm used in multi-level optimizations ; however, it is not based on Sum-of-Product form, or any specific input representation. Our experiments show that our approach is not only capable of automatically reproducing some known architectural implementations without any prior knowledge about the functionality of the circuit, but also, in some cases, it is able to discover completely new designs which we have not seen described in literature. Copyright 2009 ACM.