   allowing inlining and loop unrolling. It also algebraically simplifies
            the Halley steps leading to a big reduction in the number of floating
            point operations required compared to a "black box" implementation
            that calculates the derivatives seperately and then combines them in
            the Halley code. Typically, it was found that computation using type
            <code class="computeroutput"><span class="keyword">double</span></code> took a few times
            lo