How much exact are the operations in CGAL function "halfspace intersection with constructions"

Question

I want to compare my own algorithm with CGAL's halfspace intersection algorithm in terms of their speed performance. Since I did my own operations with double, I obtain inexact constructions of points and lines. Also I use inexact predicates. In order to get a fair comparison, I also want CGAL's operations to work with double, to produce inexact constructions and to use inexact predicates. I chose Simple_cartesian<double> kernel, defined my planes with this kernel and declared my variable to hold the output mesh as Surface_mesh of this kernel's points. I call halfspace_intersection_with_construction_3() function I am still not sure whether these specifications are sufficient for CGAL to do everything inexact? I am suspecious of whether it changes operations to exact forms to be robust despete my specifications. The reason I think so is I get almost the same speed performance with the version where I use exact_predicates_inexact_constructions kernel. Should I give some traits class as argument? Actually I did not understand much how the traits class work.