  In order to obtain the analytic expression of an amplitude from a generic
CHY-integrand, a new algorithm based on the so-called cross-ratio identities
has been proposed recently. In this paper, we apply this new approach to a
variety of theories including: non-linear sigma model, special Galileon theory,
pure Yang-Mills theory, pure gravity, Born-Infeld theory, Dirac-Born-Infeld
theory and its extension, Yang-Mills-scalar theory, Einstein-Maxwell theory as
well as Einstein-Yang-Mills theory. CHY-integrands of these theories which
contain higher-order poles can be calculated conveniently by using the
cross-ratio identity method, and all results above have been verified
numerically.
