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Automated techniques for analyzing floating-point code for roundoff error as well as control-flow instability are of growing importance. It is important to compute rigorous estimates of roundoff error, as well as determine the extent of control-flow instability due to roundoff error flowing into conditional statements. Currently available analysis techniques are either non-rigorous or do not produce tight roundoff error bounds in many practical situations. Our approach embodied in a new tool called \seesaw employs {\em symbolic reverse-mode automatic differentiation}, smoothly handling conditionals, and offering tight error bounds. Key steps in \seesaw include weakening conditionals to accommodate roundoff error, computing a symbolic error function that depends on program paths taken, and optimizing this function whose domain may be non-rectangular by paving it with a rectangle-based cover. Our benchmarks cover many practical examples for which such rigorous analysis has hitherto not been applied, or has yielded inferior results. 

Automated techniques for analyzing floating-point code for roundoff error as well as control-flow instability are of growing importance. It is important to compute rigorous estimates of roundoff error, as well as determine the extent of control-flow instability due to roundoff error flowing into conditional statements. Currently available analysis techniques are either non-rigorous or do not produce tight roundoff error bounds in many practical situations. Our approach embodied in a new tool called \seesaw employs {\em symbolic reverse-mode automatic differentiation}, smoothly handling conditionals, and offering tight error bounds. Key steps in \seesaw include weakening conditionals to accommodate roundoff error, computing a symbolic error function that depends on program paths taken, and optimizing this function whose domain may be non-rectangular by paving it with a rectangle-based cover. Our benchmarks cover many practical examples for which such rigorous analysis has hitherto not been applied, or has yielded inferior results.