Average Error: 58.1 → 58.1
Time: 18.7s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left(77617 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}\]
\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 r59919 = 333.75;
        double r59920 = 33096.0;
        double r59921 = 6.0;
        double r59922 = pow(r59920, r59921);
        double r59923 = r59919 * r59922;
        double r59924 = 77617.0;
        double r59925 = r59924 * r59924;
        double r59926 = 11.0;
        double r59927 = r59926 * r59925;
        double r59928 = r59920 * r59920;
        double r59929 = r59927 * r59928;
        double r59930 = -r59922;
        double r59931 = r59929 + r59930;
        double r59932 = -121.0;
        double r59933 = 4.0;
        double r59934 = pow(r59920, r59933);
        double r59935 = r59932 * r59934;
        double r59936 = r59931 + r59935;
        double r59937 = -2.0;
        double r59938 = r59936 + r59937;
        double r59939 = r59925 * r59938;
        double r59940 = r59923 + r59939;
        double r59941 = 5.5;
        double r59942 = 8.0;
        double r59943 = pow(r59920, r59942);
        double r59944 = r59941 * r59943;
        double r59945 = r59940 + r59944;
        double r59946 = 2.0;
        double r59947 = r59946 * r59920;
        double r59948 = r59924 / r59947;
        double r59949 = r59945 + r59948;
        return r59949;
}
↓
double f() {
        double r59950 = 77617.0;
        double r59951 = r59950 * r59950;
        double r59952 = -2.0;
        double r59953 = -121.0;
        double r59954 = 33096.0;
        double r59955 = 4.0;
        double r59956 = pow(r59954, r59955);
        double r59957 = 11.0;
        double r59958 = r59957 * r59951;
        double r59959 = r59954 * r59954;
        double r59960 = r59958 * r59959;
        double r59961 = 6.0;
        double r59962 = pow(r59954, r59961);
        double r59963 = r59960 - r59962;
        double r59964 = fma(r59953, r59956, r59963);
        double r59965 = r59952 + r59964;
        double r59966 = 333.75;
        double r59967 = 5.5;
        double r59968 = 8.0;
        double r59969 = pow(r59954, r59968);
        double r59970 = 2.0;
        double r59971 = r59970 * r59954;
        double r59972 = r59950 / r59971;
        double r59973 = fma(r59967, r59969, r59972);
        double r59974 = fma(r59962, r59966, r59973);
        double r59975 = fma(r59951, r59965, r59974);
        double r59976 = 3.0;
        double r59977 = pow(r59975, r59976);
        double r59978 = cbrt(r59977);
        return r59978;
}

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 2019325 +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))))