Mixing Condition Numbers and Oracles for Accurate Floating-point Debugging

Recent advances have made numeric debugging tools much faster by using double-double oracles, and numeric analysis tools much more accurate by using condition numbers. But these techniques have downsides: double-double oracles have correlated error so miss floating-point errors while condition numbers cannot cleanly handle over- and underflow. We combine both techniques to avoid these downsides. Our combination, Explanifloat,computes condition numbers using double-double arithmetic, which avoids correlated errors. To handle over-and underflow, it introduces a separate logarithmic oracle. As a result, Explanifloatachieves a precision of 80.0% and a recall of 96.1 % on a collection of 546 difficult numeric benchmarks: more accurate than double-double oracles yet dramatically faster than arbitrary-precision condition number computations.