  One of the necessary steps in constructing high precision option of KKMC was
to install the double bremsstrahlung matrix element for the process e+ e- to
nu_e bar nu_e into the scheme of Coherent Exclusive Exponentiation. The process
is also interesting because of gauge cancellation of contributions for photon
emission from incoming fermion lines and t-channel W. The QED U(1) gauge
properties require terms of the triple and quatric gauge couplings to be taken
into considerations as well. Thanks to expansion starting from the
approximation of contact interaction, good example to study the internal
structure of the amplitude is available.
  In the developed scheme, natural separation of the complete amplitude into
gauge invariant parts is straightforward. Each part has well defined physical
interpretation, which after partial integration over phase space provides
terms: infrared singular, leading log, next-to-leading-log, etc. Contributions
related to triple and quatric gauge coupling of W (extracted with the help of
expansion around contact W-interaction), have been ordered as well. The
separation is also helpful, to define extrapolation/reduction procedure of CEEX
exponentiation for the nu_e channel.
