Well the title is a little misleading but exact.<p>It is much more we finally have a reliable&#x2F;proven way for estimating errors in floating point arithmetic for transcendental? operations notably on Intel platform.<p>Which is both impressive and important, and makes me wonder why it took so many times to appear while we use PC computers since so many years for non linear system with error amplifications (risk assessment, turbulent flows, n body problem).<p>I am like kind of surprised we make more and more use of computers for data crunching, that we give more and more precision on the results but few consider to check the exactitude : that results are less in value than the resulting errors propagated by all approximations.<p>It casts doubt on the seriousness of the industry.