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 r70744 = 333.75;
        double r70745 = 33096.0;
        double r70746 = 6.0;
        double r70747 = pow(r70745, r70746);
        double r70748 = r70744 * r70747;
        double r70749 = 77617.0;
        double r70750 = r70749 * r70749;
        double r70751 = 11.0;
        double r70752 = r70751 * r70750;
        double r70753 = r70745 * r70745;
        double r70754 = r70752 * r70753;
        double r70755 = -r70747;
        double r70756 = r70754 + r70755;
        double r70757 = -121.0;
        double r70758 = 4.0;
        double r70759 = pow(r70745, r70758);
        double r70760 = r70757 * r70759;
        double r70761 = r70756 + r70760;
        double r70762 = -2.0;
        double r70763 = r70761 + r70762;
        double r70764 = r70750 * r70763;
        double r70765 = r70748 + r70764;
        double r70766 = 5.5;
        double r70767 = 8.0;
        double r70768 = pow(r70745, r70767);
        double r70769 = r70766 * r70768;
        double r70770 = r70765 + r70769;
        double r70771 = 2.0;
        double r70772 = r70771 * r70745;
        double r70773 = r70749 / r70772;
        double r70774 = r70770 + r70773;
        return r70774;
}
↓
double f() {
        double r70775 = 77617.0;
        double r70776 = 11.0;
        double r70777 = r70775 * r70775;
        double r70778 = r70776 * r70777;
        double r70779 = 33096.0;
        double r70780 = r70779 * r70779;
        double r70781 = r70778 * r70780;
        double r70782 = 6.0;
        double r70783 = pow(r70779, r70782);
        double r70784 = 4.0;
        double r70785 = pow(r70779, r70784);
        double r70786 = -121.0;
        double r70787 = -2.0;
        double r70788 = fma(r70785, r70786, r70787);
        double r70789 = r70783 - r70788;
        double r70790 = r70781 - r70789;
        double r70791 = r70775 * r70790;
        double r70792 = 333.75;
        double r70793 = 8.0;
        double r70794 = pow(r70779, r70793);
        double r70795 = 5.5;
        double r70796 = 2.0;
        double r70797 = r70796 * r70779;
        double r70798 = r70775 / r70797;
        double r70799 = fma(r70794, r70795, r70798);
        double r70800 = fma(r70792, r70783, r70799);
        double r70801 = fma(r70775, r70791, r70800);
        return r70801;
}

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 2020024 +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))))