Average Error: 58.1 → 58.1
Time: 2.5s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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}
↓
\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)
double f() {
        double r58896 = 333.75;
        double r58897 = 33096.0;
        double r58898 = 6.0;
        double r58899 = pow(r58897, r58898);
        double r58900 = r58896 * r58899;
        double r58901 = 77617.0;
        double r58902 = r58901 * r58901;
        double r58903 = 11.0;
        double r58904 = r58903 * r58902;
        double r58905 = r58897 * r58897;
        double r58906 = r58904 * r58905;
        double r58907 = -r58899;
        double r58908 = r58906 + r58907;
        double r58909 = -121.0;
        double r58910 = 4.0;
        double r58911 = pow(r58897, r58910);
        double r58912 = r58909 * r58911;
        double r58913 = r58908 + r58912;
        double r58914 = -2.0;
        double r58915 = r58913 + r58914;
        double r58916 = r58902 * r58915;
        double r58917 = r58900 + r58916;
        double r58918 = 5.5;
        double r58919 = 8.0;
        double r58920 = pow(r58897, r58919);
        double r58921 = r58918 * r58920;
        double r58922 = r58917 + r58921;
        double r58923 = 2.0;
        double r58924 = r58923 * r58897;
        double r58925 = r58901 / r58924;
        double r58926 = r58922 + r58925;
        return r58926;
}
↓
double f() {
        double r58927 = 77617.0;
        double r58928 = 11.0;
        double r58929 = r58927 * r58927;
        double r58930 = r58928 * r58929;
        double r58931 = 33096.0;
        double r58932 = r58931 * r58931;
        double r58933 = r58930 * r58932;
        double r58934 = 6.0;
        double r58935 = pow(r58931, r58934);
        double r58936 = 4.0;
        double r58937 = pow(r58931, r58936);
        double r58938 = -121.0;
        double r58939 = -2.0;
        double r58940 = fma(r58937, r58938, r58939);
        double r58941 = r58935 - r58940;
        double r58942 = r58933 - r58941;
        double r58943 = r58927 * r58942;
        double r58944 = 333.75;
        double r58945 = 8.0;
        double r58946 = pow(r58931, r58945);
        double r58947 = 5.5;
        double r58948 = 2.0;
        double r58949 = r58948 * r58931;
        double r58950 = r58927 / r58949;
        double r58951 = fma(r58946, r58947, r58950);
        double r58952 = fma(r58944, r58935, r58951);
        double r58953 = fma(r58927, r58943, r58952);
        return r58953;
}

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. Simplified58.1

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

  4. Final simplification58.1

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

Reproduce

herbie shell --seed 2020039 +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))))