Average Error: 58.1 → 58.1
Time: 18.4s
Precision: 64
\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left(77617 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}\]
\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}
↓
\sqrt[3]{{\left(\mathsf{fma}\left(77617 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}
double f() {
        double r73623 = 333.75;
        double r73624 = 33096.0;
        double r73625 = 6.0;
        double r73626 = pow(r73624, r73625);
        double r73627 = r73623 * r73626;
        double r73628 = 77617.0;
        double r73629 = r73628 * r73628;
        double r73630 = 11.0;
        double r73631 = r73630 * r73629;
        double r73632 = r73624 * r73624;
        double r73633 = r73631 * r73632;
        double r73634 = -r73626;
        double r73635 = r73633 + r73634;
        double r73636 = -121.0;
        double r73637 = 4.0;
        double r73638 = pow(r73624, r73637);
        double r73639 = r73636 * r73638;
        double r73640 = r73635 + r73639;
        double r73641 = -2.0;
        double r73642 = r73640 + r73641;
        double r73643 = r73629 * r73642;
        double r73644 = r73627 + r73643;
        double r73645 = 5.5;
        double r73646 = 8.0;
        double r73647 = pow(r73624, r73646);
        double r73648 = r73645 * r73647;
        double r73649 = r73644 + r73648;
        double r73650 = 2.0;
        double r73651 = r73650 * r73624;
        double r73652 = r73628 / r73651;
        double r73653 = r73649 + r73652;
        return r73653;
}
↓
double f() {
        double r73654 = 77617.0;
        double r73655 = r73654 * r73654;
        double r73656 = -2.0;
        double r73657 = -121.0;
        double r73658 = 33096.0;
        double r73659 = 4.0;
        double r73660 = pow(r73658, r73659);
        double r73661 = 11.0;
        double r73662 = r73661 * r73655;
        double r73663 = r73658 * r73658;
        double r73664 = r73662 * r73663;
        double r73665 = 6.0;
        double r73666 = pow(r73658, r73665);
        double r73667 = r73664 - r73666;
        double r73668 = fma(r73657, r73660, r73667);
        double r73669 = r73656 + r73668;
        double r73670 = 333.75;
        double r73671 = 5.5;
        double r73672 = 8.0;
        double r73673 = pow(r73658, r73672);
        double r73674 = 2.0;
        double r73675 = r73674 * r73658;
        double r73676 = r73654 / r73675;
        double r73677 = fma(r73671, r73673, r73676);
        double r73678 = fma(r73666, r73670, r73677);
        double r73679 = fma(r73655, r73669, r73678);
        double r73680 = 3.0;
        double r73681 = pow(r73679, r73680);
        double r73682 = cbrt(r73681);
        return r73682;
}

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. Using strategy rm

  3. Applied add-cbrt-cube58.1

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\right) \cdot \left(\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\right)\right) \cdot \left(\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096}\right)}}\]

  4. Simplified58.1

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\mathsf{fma}\left(77617 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}}\]

  5. Final simplification58.1

    \[\leadsto \sqrt[3]{{\left(\mathsf{fma}\left(77617 \cdot 77617, -2 + \mathsf{fma}\left(-121, {33096}^{4}, \left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) - {33096}^{6}\right), \mathsf{fma}\left({33096}^{6}, 333.75, \mathsf{fma}\left(5.5, {33096}^{8}, \frac{77617}{2 \cdot 33096}\right)\right)\right)\right)}^{3}}\]

Reproduce

herbie shell --seed 2019303 +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))))