Average Error: 58.1 → 58.1
Time: 10.8s
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 r2597684 = 333.75;
        double r2597685 = 33096.0;
        double r2597686 = 6.0;
        double r2597687 = pow(r2597685, r2597686);
        double r2597688 = r2597684 * r2597687;
        double r2597689 = 77617.0;
        double r2597690 = r2597689 * r2597689;
        double r2597691 = 11.0;
        double r2597692 = r2597691 * r2597690;
        double r2597693 = r2597685 * r2597685;
        double r2597694 = r2597692 * r2597693;
        double r2597695 = -r2597687;
        double r2597696 = r2597694 + r2597695;
        double r2597697 = -121.0;
        double r2597698 = 4.0;
        double r2597699 = pow(r2597685, r2597698);
        double r2597700 = r2597697 * r2597699;
        double r2597701 = r2597696 + r2597700;
        double r2597702 = -2.0;
        double r2597703 = r2597701 + r2597702;
        double r2597704 = r2597690 * r2597703;
        double r2597705 = r2597688 + r2597704;
        double r2597706 = 5.5;
        double r2597707 = 8.0;
        double r2597708 = pow(r2597685, r2597707);
        double r2597709 = r2597706 * r2597708;
        double r2597710 = r2597705 + r2597709;
        double r2597711 = 2.0;
        double r2597712 = r2597711 * r2597685;
        double r2597713 = r2597689 / r2597712;
        double r2597714 = r2597710 + r2597713;
        return r2597714;
}
↓
double f() {
        double r2597715 = 77617.0;
        double r2597716 = r2597715 * r2597715;
        double r2597717 = 33096.0;
        double r2597718 = r2597715 * r2597717;
        double r2597719 = r2597718 * r2597718;
        double r2597720 = 11.0;
        double r2597721 = 4.0;
        double r2597722 = pow(r2597717, r2597721);
        double r2597723 = -121.0;
        double r2597724 = -2.0;
        double r2597725 = 6.0;
        double r2597726 = pow(r2597717, r2597725);
        double r2597727 = r2597724 - r2597726;
        double r2597728 = fma(r2597722, r2597723, r2597727);
        double r2597729 = fma(r2597719, r2597720, r2597728);
        double r2597730 = 333.75;
        double r2597731 = 8.0;
        double r2597732 = pow(r2597717, r2597731);
        double r2597733 = 5.5;
        double r2597734 = r2597715 / r2597717;
        double r2597735 = 2.0;
        double r2597736 = r2597734 / r2597735;
        double r2597737 = fma(r2597732, r2597733, r2597736);
        double r2597738 = fma(r2597730, r2597726, r2597737);
        double r2597739 = fma(r2597716, r2597729, r2597738);
        return r2597739;
}

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 2019171 +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))))