Regarding the bounding of numerical results, we currently have precise method that cannot be used on real size applications and methods that can be used at scal

Regarding the bounding of numerical results, we currently have precise method that cannot be used on real size applications and methods that can be used at scale but tend to tell you that your result is between minus infinity and plus infinity. I have seen it used sucessfully in small math kernel and embedded systems but genuine application usually require deep modifications of the algorithms to get any useful result.