We present a system for the automatic synthesis of efficient algorithms specialized for a particular memory hierarchy and a set of storage devices. The developer provides two independent inputs: 1) an algorithm that ignores memory hierarchy and external storage aspects; and 2) a description of the target memory hierarchy, including its topology and parameters. Our system is able to automatically synthesize memory-hierarchy and storage-device-aware algorithms out of those specifications, for tasks such as joins and sorting. The framework is extensible and allows developers to quickly synthesize custom out-of-core algorithms as new storage technologies become available.