Average Error: 58.1 → 58.1
Time: 10.9s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617 \cdot 77617, \mathsf{fma}\left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right), 11, \mathsf{fma}\left({33096}^{4}, -121, -2 - {33096}^{6}\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{\frac{77617}{33096}}{2}\right)\right)\right)\]
\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 \cdot 77617, \mathsf{fma}\left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right), 11, \mathsf{fma}\left({33096}^{4}, -121, -2 - {33096}^{6}\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{\frac{77617}{33096}}{2}\right)\right)\right)
double f() {
        double r2923916 = 333.75;
        double r2923917 = 33096.0;
        double r2923918 = 6.0;
        double r2923919 = pow(r2923917, r2923918);
        double r2923920 = r2923916 * r2923919;
        double r2923921 = 77617.0;
        double r2923922 = r2923921 * r2923921;
        double r2923923 = 11.0;
        double r2923924 = r2923923 * r2923922;
        double r2923925 = r2923917 * r2923917;
        double r2923926 = r2923924 * r2923925;
        double r2923927 = -r2923919;
        double r2923928 = r2923926 + r2923927;
        double r2923929 = -121.0;
        double r2923930 = 4.0;
        double r2923931 = pow(r2923917, r2923930);
        double r2923932 = r2923929 * r2923931;
        double r2923933 = r2923928 + r2923932;
        double r2923934 = -2.0;
        double r2923935 = r2923933 + r2923934;
        double r2923936 = r2923922 * r2923935;
        double r2923937 = r2923920 + r2923936;
        double r2923938 = 5.5;
        double r2923939 = 8.0;
        double r2923940 = pow(r2923917, r2923939);
        double r2923941 = r2923938 * r2923940;
        double r2923942 = r2923937 + r2923941;
        double r2923943 = 2.0;
        double r2923944 = r2923943 * r2923917;
        double r2923945 = r2923921 / r2923944;
        double r2923946 = r2923942 + r2923945;
        return r2923946;
}
↓
double f() {
        double r2923947 = 77617.0;
        double r2923948 = r2923947 * r2923947;
        double r2923949 = 33096.0;
        double r2923950 = r2923947 * r2923949;
        double r2923951 = r2923950 * r2923950;
        double r2923952 = 11.0;
        double r2923953 = 4.0;
        double r2923954 = pow(r2923949, r2923953);
        double r2923955 = -121.0;
        double r2923956 = -2.0;
        double r2923957 = 6.0;
        double r2923958 = pow(r2923949, r2923957);
        double r2923959 = r2923956 - r2923958;
        double r2923960 = fma(r2923954, r2923955, r2923959);
        double r2923961 = fma(r2923951, r2923952, r2923960);
        double r2923962 = 333.75;
        double r2923963 = 8.0;
        double r2923964 = pow(r2923949, r2923963);
        double r2923965 = 5.5;
        double r2923966 = r2923947 / r2923949;
        double r2923967 = 2.0;
        double r2923968 = r2923966 / r2923967;
        double r2923969 = fma(r2923964, r2923965, r2923968);
        double r2923970 = fma(r2923962, r2923958, r2923969);
        double r2923971 = fma(r2923948, r2923961, r2923970);
        return r2923971;
}

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

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

  3. Final simplification58.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  (+ (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) (/ 77617.0 (* 2.0 33096.0))))