While the reconstruction of the control-flow graph of a binary has received wide attention, the challenge of categorizing code into defect-free and possibly incorrect remains a challenge for current static analyses. We present the intermediate language RREIL and a corresponding analysis framework that is able to infer precise numeric information on variables without resorting to an expensive analysis at the bit-level. Specifically, we propose a hierarchy of three interfaces to abstract domains, namely for inferring memory layout, bit-level information and numeric information. Our framework can be easily enriched with new abstract domains at each level. We demonstrate the extensibility of our framework by detailing a novel acceleration technique (a so-called widening) as an abstract domain that helps to find precise fixpoints of loops.