  Can we assure math computations by automatic verifying floating-point
accuracy? We define fast arithmetic (based on Dekker [1971]) over twofold
approximations $z\approx z_0+z_1$, such that $z_0$ is standard result and $z_1$
assesses inaccuracy $\Delta z_0=z-z_0$. We propose on-fly tracking $z_1$,
detecting if $\Delta z_0$ appears too high. We believe permanent tracking is
worth its cost. C++ test code for Intel AVX available via web.
