Average Error: 58.1 → 58.1
Time: 2.5s
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 r64795 = 333.75;
        double r64796 = 33096.0;
        double r64797 = 6.0;
        double r64798 = pow(r64796, r64797);
        double r64799 = r64795 * r64798;
        double r64800 = 77617.0;
        double r64801 = r64800 * r64800;
        double r64802 = 11.0;
        double r64803 = r64802 * r64801;
        double r64804 = r64796 * r64796;
        double r64805 = r64803 * r64804;
        double r64806 = -r64798;
        double r64807 = r64805 + r64806;
        double r64808 = -121.0;
        double r64809 = 4.0;
        double r64810 = pow(r64796, r64809);
        double r64811 = r64808 * r64810;
        double r64812 = r64807 + r64811;
        double r64813 = -2.0;
        double r64814 = r64812 + r64813;
        double r64815 = r64801 * r64814;
        double r64816 = r64799 + r64815;
        double r64817 = 5.5;
        double r64818 = 8.0;
        double r64819 = pow(r64796, r64818);
        double r64820 = r64817 * r64819;
        double r64821 = r64816 + r64820;
        double r64822 = 2.0;
        double r64823 = r64822 * r64796;
        double r64824 = r64800 / r64823;
        double r64825 = r64821 + r64824;
        return r64825;
}
↓
double f() {
        double r64826 = 77617.0;
        double r64827 = 11.0;
        double r64828 = r64826 * r64826;
        double r64829 = r64827 * r64828;
        double r64830 = 33096.0;
        double r64831 = r64830 * r64830;
        double r64832 = r64829 * r64831;
        double r64833 = 6.0;
        double r64834 = pow(r64830, r64833);
        double r64835 = 4.0;
        double r64836 = pow(r64830, r64835);
        double r64837 = -121.0;
        double r64838 = -2.0;
        double r64839 = fma(r64836, r64837, r64838);
        double r64840 = r64834 - r64839;
        double r64841 = r64832 - r64840;
        double r64842 = r64826 * r64841;
        double r64843 = 333.75;
        double r64844 = 8.0;
        double r64845 = pow(r64830, r64844);
        double r64846 = 5.5;
        double r64847 = 2.0;
        double r64848 = r64847 * r64830;
        double r64849 = r64826 / r64848;
        double r64850 = fma(r64845, r64846, r64849);
        double r64851 = fma(r64843, r64834, r64850);
        double r64852 = fma(r64826, r64842, r64851);
        return r64852;
}

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 2020060 +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))))