conclusion.txt

Conclusion1:
all the hiccups in all the graphs are due to one of these:

-a case where dxi and der(xi) have same dir while dxP does not  ==> use dxP
-a case in iterations in updateQ where a small d/h is found     ==> do not use iterations for update Q or inhance to avoid small d.
-cases in analytic simultaneous updates where near eqilibruim or root finding fails in an untamed quadrature equation.  ==> use iterations for simultaneous updates

Conclusion2:

It is obvious in all graphs that A_expr is more efficient than A_manual