Ray tracing of implicit surfaces suffers of reliability problems: when an Implicit Surface is ray traced without guaranteed methods, thin details of the surface are not rendered correctly. The current guaranteed methods, although simple to implement, are slower than not reliable methods. This paper shows a guaranteed method that uses interval analysis to obtain extra-information of the surfaces. This information allows to determine complicated regions in which more work has to be done to obtain antialiased images, avoiding unnecessary work in other less problematic areas. This method reduces the time required to render implicit surfaces, obtaining images with the same quality of other methods in which a regular number of rays are traced per pixel.