Average Error: 58.1 → 58.1
Time: 2.7s
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 r60883 = 333.75;
        double r60884 = 33096.0;
        double r60885 = 6.0;
        double r60886 = pow(r60884, r60885);
        double r60887 = r60883 * r60886;
        double r60888 = 77617.0;
        double r60889 = r60888 * r60888;
        double r60890 = 11.0;
        double r60891 = r60890 * r60889;
        double r60892 = r60884 * r60884;
        double r60893 = r60891 * r60892;
        double r60894 = -r60886;
        double r60895 = r60893 + r60894;
        double r60896 = -121.0;
        double r60897 = 4.0;
        double r60898 = pow(r60884, r60897);
        double r60899 = r60896 * r60898;
        double r60900 = r60895 + r60899;
        double r60901 = -2.0;
        double r60902 = r60900 + r60901;
        double r60903 = r60889 * r60902;
        double r60904 = r60887 + r60903;
        double r60905 = 5.5;
        double r60906 = 8.0;
        double r60907 = pow(r60884, r60906);
        double r60908 = r60905 * r60907;
        double r60909 = r60904 + r60908;
        double r60910 = 2.0;
        double r60911 = r60910 * r60884;
        double r60912 = r60888 / r60911;
        double r60913 = r60909 + r60912;
        return r60913;
}
↓
double f() {
        double r60914 = 77617.0;
        double r60915 = 11.0;
        double r60916 = r60914 * r60914;
        double r60917 = r60915 * r60916;
        double r60918 = 33096.0;
        double r60919 = r60918 * r60918;
        double r60920 = r60917 * r60919;
        double r60921 = 6.0;
        double r60922 = pow(r60918, r60921);
        double r60923 = 4.0;
        double r60924 = pow(r60918, r60923);
        double r60925 = -121.0;
        double r60926 = -2.0;
        double r60927 = fma(r60924, r60925, r60926);
        double r60928 = r60922 - r60927;
        double r60929 = r60920 - r60928;
        double r60930 = r60914 * r60929;
        double r60931 = 333.75;
        double r60932 = 8.0;
        double r60933 = pow(r60918, r60932);
        double r60934 = 5.5;
        double r60935 = 2.0;
        double r60936 = r60935 * r60918;
        double r60937 = r60914 / r60936;
        double r60938 = fma(r60933, r60934, r60937);
        double r60939 = fma(r60931, r60922, r60938);
        double r60940 = fma(r60914, r60930, r60939);
        double r60941 = 3.0;
        double r60942 = pow(r60940, r60941);
        double r60943 = cbrt(r60942);
        return r60943;
}

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 2020060 +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))))