Average Error: 58.1 → 58.1
Time: 16.1s
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 r34601 = 333.75;
        double r34602 = 33096.0;
        double r34603 = 6.0;
        double r34604 = pow(r34602, r34603);
        double r34605 = r34601 * r34604;
        double r34606 = 77617.0;
        double r34607 = r34606 * r34606;
        double r34608 = 11.0;
        double r34609 = r34608 * r34607;
        double r34610 = r34602 * r34602;
        double r34611 = r34609 * r34610;
        double r34612 = -r34604;
        double r34613 = r34611 + r34612;
        double r34614 = -121.0;
        double r34615 = 4.0;
        double r34616 = pow(r34602, r34615);
        double r34617 = r34614 * r34616;
        double r34618 = r34613 + r34617;
        double r34619 = -2.0;
        double r34620 = r34618 + r34619;
        double r34621 = r34607 * r34620;
        double r34622 = r34605 + r34621;
        double r34623 = 5.5;
        double r34624 = 8.0;
        double r34625 = pow(r34602, r34624);
        double r34626 = r34623 * r34625;
        double r34627 = r34622 + r34626;
        double r34628 = 2.0;
        double r34629 = r34628 * r34602;
        double r34630 = r34606 / r34629;
        double r34631 = r34627 + r34630;
        return r34631;
}
↓
double f() {
        double r34632 = 77617.0;
        double r34633 = r34632 * r34632;
        double r34634 = -2.0;
        double r34635 = -121.0;
        double r34636 = 33096.0;
        double r34637 = 4.0;
        double r34638 = pow(r34636, r34637);
        double r34639 = 11.0;
        double r34640 = r34639 * r34633;
        double r34641 = r34636 * r34636;
        double r34642 = r34640 * r34641;
        double r34643 = 6.0;
        double r34644 = pow(r34636, r34643);
        double r34645 = r34642 - r34644;
        double r34646 = fma(r34635, r34638, r34645);
        double r34647 = r34634 + r34646;
        double r34648 = 333.75;
        double r34649 = 5.5;
        double r34650 = 8.0;
        double r34651 = pow(r34636, r34650);
        double r34652 = 2.0;
        double r34653 = r34652 * r34636;
        double r34654 = r34632 / r34653;
        double r34655 = fma(r34649, r34651, r34654);
        double r34656 = fma(r34644, r34648, r34655);
        double r34657 = fma(r34633, r34647, r34656);
        double r34658 = 3.0;
        double r34659 = pow(r34657, r34658);
        double r34660 = cbrt(r34659);
        return r34660;
}

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 2019306 +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))))