Average Error: 58.1 → 58.1
Time: 11.0s
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 r2238750 = 333.75;
        double r2238751 = 33096.0;
        double r2238752 = 6.0;
        double r2238753 = pow(r2238751, r2238752);
        double r2238754 = r2238750 * r2238753;
        double r2238755 = 77617.0;
        double r2238756 = r2238755 * r2238755;
        double r2238757 = 11.0;
        double r2238758 = r2238757 * r2238756;
        double r2238759 = r2238751 * r2238751;
        double r2238760 = r2238758 * r2238759;
        double r2238761 = -r2238753;
        double r2238762 = r2238760 + r2238761;
        double r2238763 = -121.0;
        double r2238764 = 4.0;
        double r2238765 = pow(r2238751, r2238764);
        double r2238766 = r2238763 * r2238765;
        double r2238767 = r2238762 + r2238766;
        double r2238768 = -2.0;
        double r2238769 = r2238767 + r2238768;
        double r2238770 = r2238756 * r2238769;
        double r2238771 = r2238754 + r2238770;
        double r2238772 = 5.5;
        double r2238773 = 8.0;
        double r2238774 = pow(r2238751, r2238773);
        double r2238775 = r2238772 * r2238774;
        double r2238776 = r2238771 + r2238775;
        double r2238777 = 2.0;
        double r2238778 = r2238777 * r2238751;
        double r2238779 = r2238755 / r2238778;
        double r2238780 = r2238776 + r2238779;
        return r2238780;
}
↓
double f() {
        double r2238781 = 77617.0;
        double r2238782 = r2238781 * r2238781;
        double r2238783 = 33096.0;
        double r2238784 = r2238781 * r2238783;
        double r2238785 = r2238784 * r2238784;
        double r2238786 = 11.0;
        double r2238787 = 4.0;
        double r2238788 = pow(r2238783, r2238787);
        double r2238789 = -121.0;
        double r2238790 = -2.0;
        double r2238791 = 6.0;
        double r2238792 = pow(r2238783, r2238791);
        double r2238793 = r2238790 - r2238792;
        double r2238794 = fma(r2238788, r2238789, r2238793);
        double r2238795 = fma(r2238785, r2238786, r2238794);
        double r2238796 = 333.75;
        double r2238797 = 8.0;
        double r2238798 = pow(r2238783, r2238797);
        double r2238799 = 5.5;
        double r2238800 = r2238781 / r2238783;
        double r2238801 = 2.0;
        double r2238802 = r2238800 / r2238801;
        double r2238803 = fma(r2238798, r2238799, r2238802);
        double r2238804 = fma(r2238796, r2238792, r2238803);
        double r2238805 = fma(r2238782, r2238795, r2238804);
        return r2238805;
}

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 2019172 +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))))