Average Error: 58.1 → 58.1
Time: 2.6s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}\]
\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}
↓
\sqrt[3]{{\left(\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}
double f() {
        double r68707 = 333.75;
        double r68708 = 33096.0;
        double r68709 = 6.0;
        double r68710 = pow(r68708, r68709);
        double r68711 = r68707 * r68710;
        double r68712 = 77617.0;
        double r68713 = r68712 * r68712;
        double r68714 = 11.0;
        double r68715 = r68714 * r68713;
        double r68716 = r68708 * r68708;
        double r68717 = r68715 * r68716;
        double r68718 = -r68710;
        double r68719 = r68717 + r68718;
        double r68720 = -121.0;
        double r68721 = 4.0;
        double r68722 = pow(r68708, r68721);
        double r68723 = r68720 * r68722;
        double r68724 = r68719 + r68723;
        double r68725 = -2.0;
        double r68726 = r68724 + r68725;
        double r68727 = r68713 * r68726;
        double r68728 = r68711 + r68727;
        double r68729 = 5.5;
        double r68730 = 8.0;
        double r68731 = pow(r68708, r68730);
        double r68732 = r68729 * r68731;
        double r68733 = r68728 + r68732;
        double r68734 = 2.0;
        double r68735 = r68734 * r68708;
        double r68736 = r68712 / r68735;
        double r68737 = r68733 + r68736;
        return r68737;
}
↓
double f() {
        double r68738 = 77617.0;
        double r68739 = 11.0;
        double r68740 = r68738 * r68738;
        double r68741 = r68739 * r68740;
        double r68742 = 33096.0;
        double r68743 = r68742 * r68742;
        double r68744 = r68741 * r68743;
        double r68745 = 6.0;
        double r68746 = pow(r68742, r68745);
        double r68747 = 4.0;
        double r68748 = pow(r68742, r68747);
        double r68749 = -121.0;
        double r68750 = -2.0;
        double r68751 = fma(r68748, r68749, r68750);
        double r68752 = r68746 - r68751;
        double r68753 = r68744 - r68752;
        double r68754 = r68738 * r68753;
        double r68755 = 333.75;
        double r68756 = 8.0;
        double r68757 = pow(r68742, r68756);
        double r68758 = 5.5;
        double r68759 = 2.0;
        double r68760 = r68759 * r68742;
        double r68761 = r68738 / r68760;
        double r68762 = fma(r68757, r68758, r68761);
        double r68763 = fma(r68755, r68746, r68762);
        double r68764 = fma(r68738, r68754, r68763);
        double r68765 = 3.0;
        double r68766 = pow(r68764, r68765);
        double r68767 = cbrt(r68766);
        return r68767;
}

Error

Derivation

  1. Initial program 58.1

    \[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]

  2. Simplified58.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(77617 \cdot 77617, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 333.75 \cdot {33096}^{6} + \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)}\]
  3. Using strategy rm

  4. Applied add-cbrt-cube58.1

    \[\leadsto \color{blue}{\sqrt[3]{\left(\mathsf{fma}\left(77617 \cdot 77617, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 333.75 \cdot {33096}^{6} + \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right) \cdot \mathsf{fma}\left(77617 \cdot 77617, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 333.75 \cdot {33096}^{6} + \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right) \cdot \mathsf{fma}\left(77617 \cdot 77617, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right), 333.75 \cdot {33096}^{6} + \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)}}\]

  5. Simplified58.1

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}}\]

  6. Final simplification58.1

    \[\leadsto \sqrt[3]{{\left(\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}\]

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  :precision binary64
  (+ (+ (+ (* 333.75 (pow 33096 6)) (* (* 77617 77617) (+ (+ (+ (* (* 11 (* 77617 77617)) (* 33096 33096)) (- (pow 33096 6))) (* -121 (pow 33096 4))) -2))) (* 5.5 (pow 33096 8))) (/ 77617 (* 2 33096))))