  We describe new developments in the OpenLoops framework based on the recently
introduced on-the-fly method. The on-the-fly approach exploits the
factorisation of one-loop diagrams into segments in order to perform various
operations, such as helicity summation, diagram merging and the reduction of
Feynman integrands in between the recursion steps for the amplitude
construction. This method significantly reduces the complexity of scattering
amplitude calculations for multi-particle processes, leading to a major
increase in CPU efficiency and numerical stability. The unification of the
reduction to scalar integrals with the amplitude construction in a single
algorithm, allows to identify problematic kinematical configurations and cure
numerical instabilities in single recursion steps. A simple permutation trick
in combination with a one-parameter expansion for a single topology, which is
now implemented to any order, eliminate rank-two Gram determinant instabilities
altogether. Due to this any-order expansion, the numerical accuracy of the
algorithm can be determined with a rescaling test. The on-the-fly algorithm is
fully implemented for double and quadruple precision, which allows for true
quadruple precision benchmarks with up to 32 correct digits as well as a
powerful rescue system for unstable points. We present first speed and
stability results for these new features. The on-the-fly algorithm is part of
the forthcoming release of OpenLoops 2.
