Average Error: 58.1 → 58.1
Time: 2.6s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617, 77617 \cdot \left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - \left({33096}^{6} - \mathsf{fma}\left({33096}^{4}, -121, -2\right)\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{77617}{2 \cdot 33096}\right)\right)\right)\]
\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 r61888 = 333.75;
        double r61889 = 33096.0;
        double r61890 = 6.0;
        double r61891 = pow(r61889, r61890);
        double r61892 = r61888 * r61891;
        double r61893 = 77617.0;
        double r61894 = r61893 * r61893;
        double r61895 = 11.0;
        double r61896 = r61895 * r61894;
        double r61897 = r61889 * r61889;
        double r61898 = r61896 * r61897;
        double r61899 = -r61891;
        double r61900 = r61898 + r61899;
        double r61901 = -121.0;
        double r61902 = 4.0;
        double r61903 = pow(r61889, r61902);
        double r61904 = r61901 * r61903;
        double r61905 = r61900 + r61904;
        double r61906 = -2.0;
        double r61907 = r61905 + r61906;
        double r61908 = r61894 * r61907;
        double r61909 = r61892 + r61908;
        double r61910 = 5.5;
        double r61911 = 8.0;
        double r61912 = pow(r61889, r61911);
        double r61913 = r61910 * r61912;
        double r61914 = r61909 + r61913;
        double r61915 = 2.0;
        double r61916 = r61915 * r61889;
        double r61917 = r61893 / r61916;
        double r61918 = r61914 + r61917;
        return r61918;
}
↓
double f() {
        double r61919 = 77617.0;
        double r61920 = 11.0;
        double r61921 = r61919 * r61919;
        double r61922 = r61920 * r61921;
        double r61923 = 33096.0;
        double r61924 = r61923 * r61923;
        double r61925 = r61922 * r61924;
        double r61926 = 6.0;
        double r61927 = pow(r61923, r61926);
        double r61928 = 4.0;
        double r61929 = pow(r61923, r61928);
        double r61930 = -121.0;
        double r61931 = -2.0;
        double r61932 = fma(r61929, r61930, r61931);
        double r61933 = r61927 - r61932;
        double r61934 = r61925 - r61933;
        double r61935 = r61919 * r61934;
        double r61936 = 333.75;
        double r61937 = 8.0;
        double r61938 = pow(r61923, r61937);
        double r61939 = 5.5;
        double r61940 = 2.0;
        double r61941 = r61940 * r61923;
        double r61942 = r61919 / r61941;
        double r61943 = fma(r61938, r61939, r61942);
        double r61944 = fma(r61936, r61927, r61943);
        double r61945 = fma(r61919, r61935, r61944);
        return r61945;
}

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 2020001 +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))))