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 r52766 = 333.75;
        double r52767 = 33096.0;
        double r52768 = 6.0;
        double r52769 = pow(r52767, r52768);
        double r52770 = r52766 * r52769;
        double r52771 = 77617.0;
        double r52772 = r52771 * r52771;
        double r52773 = 11.0;
        double r52774 = r52773 * r52772;
        double r52775 = r52767 * r52767;
        double r52776 = r52774 * r52775;
        double r52777 = -r52769;
        double r52778 = r52776 + r52777;
        double r52779 = -121.0;
        double r52780 = 4.0;
        double r52781 = pow(r52767, r52780);
        double r52782 = r52779 * r52781;
        double r52783 = r52778 + r52782;
        double r52784 = -2.0;
        double r52785 = r52783 + r52784;
        double r52786 = r52772 * r52785;
        double r52787 = r52770 + r52786;
        double r52788 = 5.5;
        double r52789 = 8.0;
        double r52790 = pow(r52767, r52789);
        double r52791 = r52788 * r52790;
        double r52792 = r52787 + r52791;
        double r52793 = 2.0;
        double r52794 = r52793 * r52767;
        double r52795 = r52771 / r52794;
        double r52796 = r52792 + r52795;
        return r52796;
}
↓
double f() {
        double r52797 = 77617.0;
        double r52798 = 11.0;
        double r52799 = r52797 * r52797;
        double r52800 = r52798 * r52799;
        double r52801 = 33096.0;
        double r52802 = r52801 * r52801;
        double r52803 = r52800 * r52802;
        double r52804 = 6.0;
        double r52805 = pow(r52801, r52804);
        double r52806 = 4.0;
        double r52807 = pow(r52801, r52806);
        double r52808 = -121.0;
        double r52809 = -2.0;
        double r52810 = fma(r52807, r52808, r52809);
        double r52811 = r52805 - r52810;
        double r52812 = r52803 - r52811;
        double r52813 = r52797 * r52812;
        double r52814 = 333.75;
        double r52815 = 8.0;
        double r52816 = pow(r52801, r52815);
        double r52817 = 5.5;
        double r52818 = 2.0;
        double r52819 = r52818 * r52801;
        double r52820 = r52797 / r52819;
        double r52821 = fma(r52816, r52817, r52820);
        double r52822 = fma(r52814, r52805, r52821);
        double r52823 = fma(r52797, r52813, r52822);
        return r52823;
}

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 2020021 +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))))