Average Error: 58.1 → 58.1
Time: 9.9s
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 r57603 = 333.75;
        double r57604 = 33096.0;
        double r57605 = 6.0;
        double r57606 = pow(r57604, r57605);
        double r57607 = r57603 * r57606;
        double r57608 = 77617.0;
        double r57609 = r57608 * r57608;
        double r57610 = 11.0;
        double r57611 = r57610 * r57609;
        double r57612 = r57604 * r57604;
        double r57613 = r57611 * r57612;
        double r57614 = -r57606;
        double r57615 = r57613 + r57614;
        double r57616 = -121.0;
        double r57617 = 4.0;
        double r57618 = pow(r57604, r57617);
        double r57619 = r57616 * r57618;
        double r57620 = r57615 + r57619;
        double r57621 = -2.0;
        double r57622 = r57620 + r57621;
        double r57623 = r57609 * r57622;
        double r57624 = r57607 + r57623;
        double r57625 = 5.5;
        double r57626 = 8.0;
        double r57627 = pow(r57604, r57626);
        double r57628 = r57625 * r57627;
        double r57629 = r57624 + r57628;
        double r57630 = 2.0;
        double r57631 = r57630 * r57604;
        double r57632 = r57608 / r57631;
        double r57633 = r57629 + r57632;
        return r57633;
}
↓
double f() {
        double r57634 = 77617.0;
        double r57635 = r57634 * r57634;
        double r57636 = -2.0;
        double r57637 = -121.0;
        double r57638 = 33096.0;
        double r57639 = 4.0;
        double r57640 = pow(r57638, r57639);
        double r57641 = 11.0;
        double r57642 = r57641 * r57635;
        double r57643 = r57638 * r57638;
        double r57644 = r57642 * r57643;
        double r57645 = 6.0;
        double r57646 = pow(r57638, r57645);
        double r57647 = r57644 - r57646;
        double r57648 = fma(r57637, r57640, r57647);
        double r57649 = r57636 + r57648;
        double r57650 = 333.75;
        double r57651 = 5.5;
        double r57652 = 8.0;
        double r57653 = pow(r57638, r57652);
        double r57654 = 2.0;
        double r57655 = r57654 * r57638;
        double r57656 = r57634 / r57655;
        double r57657 = fma(r57651, r57653, r57656);
        double r57658 = fma(r57646, r57650, r57657);
        double r57659 = fma(r57635, r57649, r57658);
        double r57660 = 3.0;
        double r57661 = pow(r57659, r57660);
        double r57662 = cbrt(r57661);
        return r57662;
}

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 2019351 +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))))