Arfa: an Agile Regime-based Floating-point Optimization Approach for Rounding Errors
This program is tentative and subject to change.
We introduce a floating-point (FP) error optimization approach called Arfa that partitions the domain $\mathcal{D}$ of an FP expression $f_e$ into \emph{regimes} and rewrites $f_e$ in each regime where $f_e$ shows larger errors. First, Arfa seeks a rewrite substitution $f_o$ with lower errors across $\mathcal{D}$, whose error distribution is plotted for effective regime inference. Next, Arfa generates an incomplete set of ordered rewrite candidates within each regime of interest, so that searching for the best rewrite substitutions is performed efficiently. Finally, Arfa selects the best rewrite substitution by inspecting the errors of top ranked rewrite candidates, with enhancing precision also considered. Experiments on 56 FPbench examples and four real-life programs show that Arfa not only reduces the maximum and average errors of $f_e$ by 4.73 and 2.08 bits on average (and up to 33 and 16 bits), but also exhibits lower errors, sometimes to a significant degree, than Herbie and PSAT.
This program is tentative and subject to change.
Thu 19 SepDisplayed time zone: Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna change
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