The Echelle SPectrograph for Rocky Exoplanets and Stable Spectral Observations (ESPRESSO) is an ultrastable spectrograph for the coudé-combined focus of the VLT. With its unprecedented capabilities (resolution up to fi 200,000, wavelength range from 380 to 780 nm; centimeter-per-second precision in wavelength calibration), ESPRESSO is a prime example of the now spreading science machine concept: a fully-integrated system carefully designed to perform direct scientific measurements on the data, in a matter of minutes from the execution of the observations. This approach is motivated by the very specific science cases of the instrument (search for terrestrial exoplanets with the radial velocity method; measure of the variation of fundamental constants using the spectral signatures of the inter-galactic medium) and is achieved by a dedicated tool for spectral analysis, the data analysis software or DAS, targeted to both stellar and quasar spectra. In this paper, we describe characteristics and performances of the DAS, with particular emphasis on the novel algorithms for stellar and quasar analysis (continuum fitting and interpretation of the absorption features).