Average Error: 58.1 → 58.1
Time: 10.6s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\mathsf{fma}\left(77617 \cdot 77617, \mathsf{fma}\left(\left(77617 \cdot 33096\right) \cdot \left(77617 \cdot 33096\right), 11, \mathsf{fma}\left({33096}^{4}, -121, -2 - {33096}^{6}\right)\right), \mathsf{fma}\left(333.75, {33096}^{6}, \mathsf{fma}\left({33096}^{8}, 5.5, \frac{\frac{77617}{33096}}{2}\right)\right)\right)\]
\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 r2460610 = 333.75;
        double r2460611 = 33096.0;
        double r2460612 = 6.0;
        double r2460613 = pow(r2460611, r2460612);
        double r2460614 = r2460610 * r2460613;
        double r2460615 = 77617.0;
        double r2460616 = r2460615 * r2460615;
        double r2460617 = 11.0;
        double r2460618 = r2460617 * r2460616;
        double r2460619 = r2460611 * r2460611;
        double r2460620 = r2460618 * r2460619;
        double r2460621 = -r2460613;
        double r2460622 = r2460620 + r2460621;
        double r2460623 = -121.0;
        double r2460624 = 4.0;
        double r2460625 = pow(r2460611, r2460624);
        double r2460626 = r2460623 * r2460625;
        double r2460627 = r2460622 + r2460626;
        double r2460628 = -2.0;
        double r2460629 = r2460627 + r2460628;
        double r2460630 = r2460616 * r2460629;
        double r2460631 = r2460614 + r2460630;
        double r2460632 = 5.5;
        double r2460633 = 8.0;
        double r2460634 = pow(r2460611, r2460633);
        double r2460635 = r2460632 * r2460634;
        double r2460636 = r2460631 + r2460635;
        double r2460637 = 2.0;
        double r2460638 = r2460637 * r2460611;
        double r2460639 = r2460615 / r2460638;
        double r2460640 = r2460636 + r2460639;
        return r2460640;
}
↓
double f() {
        double r2460641 = 77617.0;
        double r2460642 = r2460641 * r2460641;
        double r2460643 = 33096.0;
        double r2460644 = r2460641 * r2460643;
        double r2460645 = r2460644 * r2460644;
        double r2460646 = 11.0;
        double r2460647 = 4.0;
        double r2460648 = pow(r2460643, r2460647);
        double r2460649 = -121.0;
        double r2460650 = -2.0;
        double r2460651 = 6.0;
        double r2460652 = pow(r2460643, r2460651);
        double r2460653 = r2460650 - r2460652;
        double r2460654 = fma(r2460648, r2460649, r2460653);
        double r2460655 = fma(r2460645, r2460646, r2460654);
        double r2460656 = 333.75;
        double r2460657 = 8.0;
        double r2460658 = pow(r2460643, r2460657);
        double r2460659 = 5.5;
        double r2460660 = r2460641 / r2460643;
        double r2460661 = 2.0;
        double r2460662 = r2460660 / r2460661;
        double r2460663 = fma(r2460658, r2460659, r2460662);
        double r2460664 = fma(r2460656, r2460652, r2460663);
        double r2460665 = fma(r2460642, r2460655, r2460664);
        return r2460665;
}

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 2019192 +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))))