From Warwick Tucker's Validated Numerics

Average Error: 58.1 → 56.8

Time: 1.1m

Precision: 64

Math

\[\left(\left(333.75 \cdot {33096.0}^{6.0} + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(\left(\left(11.0 \cdot \left(77617.0 \cdot 77617.0\right)\right) \cdot \left(33096.0 \cdot 33096.0\right) + \left(-{33096.0}^{6.0}\right)\right) + -121.0 \cdot {33096.0}^{4.0}\right) + -2.0\right)\right) + 5.5 \cdot {33096.0}^{8.0}\right) + \frac{77617.0}{2.0 \cdot 33096.0}\]

↓

\[\frac{\frac{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) \cdot \left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0} \cdot \frac{77617.0}{2.0 \cdot 33096.0}}{\sqrt[3]{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}} \cdot \sqrt[3]{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}}}{\sqrt[3]{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}}\]

C

double f() {
        double r5930705 = 333.75;
        double r5930706 = 33096.0;
        double r5930707 = 6.0;
        double r5930708 = pow(r5930706, r5930707);
        double r5930709 = r5930705 * r5930708;
        double r5930710 = 77617.0;
        double r5930711 = r5930710 * r5930710;
        double r5930712 = 11.0;
        double r5930713 = r5930712 * r5930711;
        double r5930714 = r5930706 * r5930706;
        double r5930715 = r5930713 * r5930714;
        double r5930716 = -r5930708;
        double r5930717 = r5930715 + r5930716;
        double r5930718 = -121.0;
        double r5930719 = 4.0;
        double r5930720 = pow(r5930706, r5930719);
        double r5930721 = r5930718 * r5930720;
        double r5930722 = r5930717 + r5930721;
        double r5930723 = -2.0;
        double r5930724 = r5930722 + r5930723;
        double r5930725 = r5930711 * r5930724;
        double r5930726 = r5930709 + r5930725;
        double r5930727 = 5.5;
        double r5930728 = 8.0;
        double r5930729 = pow(r5930706, r5930728);
        double r5930730 = r5930727 * r5930729;
        double r5930731 = r5930726 + r5930730;
        double r5930732 = 2.0;
        double r5930733 = r5930732 * r5930706;
        double r5930734 = r5930710 / r5930733;
        double r5930735 = r5930731 + r5930734;
        return r5930735;
}

↓

double f() {
        double r5930736 = 333.75;
        double r5930737 = 33096.0;
        double r5930738 = 6.0;
        double r5930739 = pow(r5930737, r5930738);
        double r5930740 = r5930736 * r5930739;
        double r5930741 = 8.0;
        double r5930742 = pow(r5930737, r5930741);
        double r5930743 = 5.5;
        double r5930744 = r5930742 * r5930743;
        double r5930745 = r5930740 + r5930744;
        double r5930746 = 11.0;
        double r5930747 = 77617.0;
        double r5930748 = r5930737 * r5930747;
        double r5930749 = r5930748 * r5930748;
        double r5930750 = r5930746 * r5930749;
        double r5930751 = -2.0;
        double r5930752 = r5930750 + r5930751;
        double r5930753 = 4.0;
        double r5930754 = pow(r5930737, r5930753);
        double r5930755 = -121.0;
        double r5930756 = r5930754 * r5930755;
        double r5930757 = r5930739 - r5930756;
        double r5930758 = r5930752 - r5930757;
        double r5930759 = r5930747 * r5930747;
        double r5930760 = r5930758 * r5930759;
        double r5930761 = r5930745 + r5930760;
        double r5930762 = /* ERROR: no posit support in C */;
        double r5930763 = /* ERROR: no posit support in C */;
        double r5930764 = r5930763 * r5930763;
        double r5930765 = 2.0;
        double r5930766 = r5930765 * r5930737;
        double r5930767 = r5930747 / r5930766;
        double r5930768 = r5930767 * r5930767;
        double r5930769 = r5930764 - r5930768;
        double r5930770 = r5930763 - r5930767;
        double r5930771 = cbrt(r5930770);
        double r5930772 = r5930771 * r5930771;
        double r5930773 = r5930769 / r5930772;
        double r5930774 = r5930773 / r5930771;
        return r5930774;
}

Derivation

1. Initial program 58.1

   \[\left(\left(333.75 \cdot {33096.0}^{6.0} + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(\left(\left(11.0 \cdot \left(77617.0 \cdot 77617.0\right)\right) \cdot \left(33096.0 \cdot 33096.0\right) + \left(-{33096.0}^{6.0}\right)\right) + -121.0 \cdot {33096.0}^{4.0}\right) + -2.0\right)\right) + 5.5 \cdot {33096.0}^{8.0}\right) + \frac{77617.0}{2.0 \cdot 33096.0}\]
2. Using strategy rm

3. Applied insert-posit16 56.8

   \[\leadsto \color{blue}{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(\left(\left(11.0 \cdot \left(77617.0 \cdot 77617.0\right)\right) \cdot \left(33096.0 \cdot 33096.0\right) + \left(-{33096.0}^{6.0}\right)\right) + -121.0 \cdot {33096.0}^{4.0}\right) + -2.0\right)\right) + 5.5 \cdot {33096.0}^{8.0}\right)\right)} + \frac{77617.0}{2.0 \cdot 33096.0}\]

4. Simplified 56.8

   \[\leadsto \color{blue}{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right)} + \frac{77617.0}{2.0 \cdot 33096.0}\]
5. Using strategy rm

6. Applied flip-+ 56.8

   \[\leadsto \color{blue}{\frac{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) \cdot \left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0} \cdot \frac{77617.0}{2.0 \cdot 33096.0}}{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}}\]
7. Using strategy rm

8. Applied add-cube-cbrt 56.8

   \[\leadsto \frac{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) \cdot \left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0} \cdot \frac{77617.0}{2.0 \cdot 33096.0}}{\color{blue}{\left(\sqrt[3]{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}} \cdot \sqrt[3]{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}\right) \cdot \sqrt[3]{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}}}\]

9. Applied associate-/r* 56.8

   \[\leadsto \color{blue}{\frac{\frac{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) \cdot \left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0} \cdot \frac{77617.0}{2.0 \cdot 33096.0}}{\sqrt[3]{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}} \cdot \sqrt[3]{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}}}{\sqrt[3]{\left(\left(\left({33096.0}^{8.0} \cdot 5.5 + {33096.0}^{6.0} \cdot 333.75\right) + \left(77617.0 \cdot 77617.0\right) \cdot \left(\left(-2.0 + 11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right)\right) - \left({33096.0}^{6.0} - -121.0 \cdot {33096.0}^{4.0}\right)\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}}}\]

10. Final simplification 56.8

    \[\leadsto \frac{\frac{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) \cdot \left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0} \cdot \frac{77617.0}{2.0 \cdot 33096.0}}{\sqrt[3]{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}} \cdot \sqrt[3]{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}}}{\sqrt[3]{\left(\left(\left(333.75 \cdot {33096.0}^{6.0} + {33096.0}^{8.0} \cdot 5.5\right) + \left(\left(11.0 \cdot \left(\left(33096.0 \cdot 77617.0\right) \cdot \left(33096.0 \cdot 77617.0\right)\right) + -2.0\right) - \left({33096.0}^{6.0} - {33096.0}^{4.0} \cdot -121.0\right)\right) \cdot \left(77617.0 \cdot 77617.0\right)\right)\right) - \frac{77617.0}{2.0 \cdot 33096.0}}}\]

Reproduce

herbie shell --seed 2019165 
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  (+ (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) (/ 77617.0 (* 2.0 33096.0))))