Computing resources are fundamentally limited and sometimes an exact solution may not even exist. Thus, when implementing real-world systems, approximations are inevitable, as are the errors they introduce. The magnitude of errors is problem-dependent but higher accuracy generally comes at a cost in terms of memory, energy or runtime, effectively creating an accuracy-efficiency tradeoff. To take advantage of this tradeoff, we need to ensure that the computed results are sufficiently accurate, otherwise we risk disastrously incorrect results or system failures. Unfortunately, the current way of programming with approximations is mostly manual, and consequently costly, error prone and often produces suboptimal results.

In this talk, we present the current state of the tool Daisy which approximates numerical programs in an automated and trustworthy fashion. Daisy allows a programmer to write exact high-level code and generates an efficient implementation satisfying a given accuracy specification. We discuss Daisy’s verification techniques for bounding the effects of numerical errors, and the finite-precision approximations Daisy can synthesize fully automatically.