Average Error: 58.1 → 58.1
Time: 17.2s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left(77617 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}\]
\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 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}
double f() {
        double r60855 = 333.75;
        double r60856 = 33096.0;
        double r60857 = 6.0;
        double r60858 = pow(r60856, r60857);
        double r60859 = r60855 * r60858;
        double r60860 = 77617.0;
        double r60861 = r60860 * r60860;
        double r60862 = 11.0;
        double r60863 = r60862 * r60861;
        double r60864 = r60856 * r60856;
        double r60865 = r60863 * r60864;
        double r60866 = -r60858;
        double r60867 = r60865 + r60866;
        double r60868 = -121.0;
        double r60869 = 4.0;
        double r60870 = pow(r60856, r60869);
        double r60871 = r60868 * r60870;
        double r60872 = r60867 + r60871;
        double r60873 = -2.0;
        double r60874 = r60872 + r60873;
        double r60875 = r60861 * r60874;
        double r60876 = r60859 + r60875;
        double r60877 = 5.5;
        double r60878 = 8.0;
        double r60879 = pow(r60856, r60878);
        double r60880 = r60877 * r60879;
        double r60881 = r60876 + r60880;
        double r60882 = 2.0;
        double r60883 = r60882 * r60856;
        double r60884 = r60860 / r60883;
        double r60885 = r60881 + r60884;
        return r60885;
}
↓
double f() {
        double r60886 = 77617.0;
        double r60887 = r60886 * r60886;
        double r60888 = -2.0;
        double r60889 = -121.0;
        double r60890 = 33096.0;
        double r60891 = 4.0;
        double r60892 = pow(r60890, r60891);
        double r60893 = 11.0;
        double r60894 = r60893 * r60887;
        double r60895 = r60890 * r60890;
        double r60896 = r60894 * r60895;
        double r60897 = 6.0;
        double r60898 = pow(r60890, r60897);
        double r60899 = r60896 - r60898;
        double r60900 = fma(r60889, r60892, r60899);
        double r60901 = r60888 + r60900;
        double r60902 = 333.75;
        double r60903 = 5.5;
        double r60904 = 8.0;
        double r60905 = pow(r60890, r60904);
        double r60906 = 2.0;
        double r60907 = r60906 * r60890;
        double r60908 = r60886 / r60907;
        double r60909 = fma(r60903, r60905, r60908);
        double r60910 = fma(r60898, r60902, r60909);
        double r60911 = fma(r60887, r60901, r60910);
        double r60912 = 3.0;
        double r60913 = pow(r60911, r60912);
        double r60914 = cbrt(r60913);
        return r60914;
}

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. Using strategy rm

  3. Applied add-cbrt-cube58.1

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

  4. Simplified58.1

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

  5. Final simplification58.1

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

Reproduce

herbie shell --seed 2019323 +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))))