Singularities introduced by reduceDAEIndex

reduceIndexDAE introduces new variables to reduce the index of a DAE.

However, I guess that this may lead to numerical problems that are not due to the original DAE.

In fact, in the pendulum from DAEToolsExample, for x(t)~0 the integration fails. If in that example we set e.g. tfinal=1.5, we obtain:

Warning: Failure at t=5.055428e-01. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.796049e-15) at time t.

Can this be avoided? Is this effect due to the introduction of Dxt7t(t)?