Average Error: 58.1 → 58.1
Time: 4.2s
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 r68678 = 333.75;
        double r68679 = 33096.0;
        double r68680 = 6.0;
        double r68681 = pow(r68679, r68680);
        double r68682 = r68678 * r68681;
        double r68683 = 77617.0;
        double r68684 = r68683 * r68683;
        double r68685 = 11.0;
        double r68686 = r68685 * r68684;
        double r68687 = r68679 * r68679;
        double r68688 = r68686 * r68687;
        double r68689 = -r68681;
        double r68690 = r68688 + r68689;
        double r68691 = -121.0;
        double r68692 = 4.0;
        double r68693 = pow(r68679, r68692);
        double r68694 = r68691 * r68693;
        double r68695 = r68690 + r68694;
        double r68696 = -2.0;
        double r68697 = r68695 + r68696;
        double r68698 = r68684 * r68697;
        double r68699 = r68682 + r68698;
        double r68700 = 5.5;
        double r68701 = 8.0;
        double r68702 = pow(r68679, r68701);
        double r68703 = r68700 * r68702;
        double r68704 = r68699 + r68703;
        double r68705 = 2.0;
        double r68706 = r68705 * r68679;
        double r68707 = r68683 / r68706;
        double r68708 = r68704 + r68707;
        return r68708;
}
↓
double f() {
        double r68709 = 77617.0;
        double r68710 = 11.0;
        double r68711 = r68709 * r68709;
        double r68712 = r68710 * r68711;
        double r68713 = 33096.0;
        double r68714 = r68713 * r68713;
        double r68715 = r68712 * r68714;
        double r68716 = 6.0;
        double r68717 = pow(r68713, r68716);
        double r68718 = 4.0;
        double r68719 = pow(r68713, r68718);
        double r68720 = -121.0;
        double r68721 = -2.0;
        double r68722 = fma(r68719, r68720, r68721);
        double r68723 = r68717 - r68722;
        double r68724 = r68715 - r68723;
        double r68725 = r68709 * r68724;
        double r68726 = 333.75;
        double r68727 = 8.0;
        double r68728 = pow(r68713, r68727);
        double r68729 = 5.5;
        double r68730 = 2.0;
        double r68731 = r68730 * r68713;
        double r68732 = r68709 / r68731;
        double r68733 = fma(r68728, r68729, r68732);
        double r68734 = fma(r68726, r68717, r68733);
        double r68735 = fma(r68709, r68725, r68734);
        return r68735;
}

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 2020034 +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))))