Average Error: 1.0 → 0.0
Time: 22.6s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\left(\left(\left(\left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right) + \left(\pi \cdot \left(v \cdot v\right)\right) \cdot \pi\right) + \pi \cdot \pi\right) \cdot \frac{\sqrt[3]{\frac{4}{3}}}{\pi \cdot \left(\pi \cdot \pi\right) - \left(\left(\left(\pi \cdot v\right) \cdot v\right) \cdot \left(\left(\pi \cdot v\right) \cdot v\right)\right) \cdot \left(\left(\pi \cdot v\right) \cdot v\right)}\right) \cdot \left(\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}\right)}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
↓
\frac{\left(\left(\left(\left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right) + \left(\pi \cdot \left(v \cdot v\right)\right) \cdot \pi\right) + \pi \cdot \pi\right) \cdot \frac{\sqrt[3]{\frac{4}{3}}}{\pi \cdot \left(\pi \cdot \pi\right) - \left(\left(\left(\pi \cdot v\right) \cdot v\right) \cdot \left(\left(\pi \cdot v\right) \cdot v\right)\right) \cdot \left(\left(\pi \cdot v\right) \cdot v\right)}\right) \cdot \left(\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}\right)}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r6162618 = 4.0;
        double r6162619 = 3.0;
        double r6162620 = atan2(1.0, 0.0);
        double r6162621 = r6162619 * r6162620;
        double r6162622 = 1.0;
        double r6162623 = v;
        double r6162624 = r6162623 * r6162623;
        double r6162625 = r6162622 - r6162624;
        double r6162626 = r6162621 * r6162625;
        double r6162627 = 2.0;
        double r6162628 = 6.0;
        double r6162629 = r6162628 * r6162624;
        double r6162630 = r6162627 - r6162629;
        double r6162631 = sqrt(r6162630);
        double r6162632 = r6162626 * r6162631;
        double r6162633 = r6162618 / r6162632;
        return r6162633;
}
↓
double f(double v) {
        double r6162634 = atan2(1.0, 0.0);
        double r6162635 = v;
        double r6162636 = r6162635 * r6162635;
        double r6162637 = r6162634 * r6162636;
        double r6162638 = r6162637 * r6162637;
        double r6162639 = r6162637 * r6162634;
        double r6162640 = r6162638 + r6162639;
        double r6162641 = r6162634 * r6162634;
        double r6162642 = r6162640 + r6162641;
        double r6162643 = 1.3333333333333333;
        double r6162644 = cbrt(r6162643);
        double r6162645 = r6162634 * r6162641;
        double r6162646 = r6162634 * r6162635;
        double r6162647 = r6162646 * r6162635;
        double r6162648 = r6162647 * r6162647;
        double r6162649 = r6162648 * r6162647;
        double r6162650 = r6162645 - r6162649;
        double r6162651 = r6162644 / r6162650;
        double r6162652 = r6162642 * r6162651;
        double r6162653 = r6162644 * r6162644;
        double r6162654 = r6162652 * r6162653;
        double r6162655 = 2.0;
        double r6162656 = 6.0;
        double r6162657 = r6162656 * r6162636;
        double r6162658 = r6162655 - r6162657;
        double r6162659 = sqrt(r6162658);
        double r6162660 = r6162654 / r6162659;
        return r6162660;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 1.0

    \[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\frac{\frac{\frac{4}{3}}{\pi - \pi \cdot \left(v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.0

    \[\leadsto \frac{\frac{\frac{4}{3}}{\color{blue}{1 \cdot \left(\pi - \pi \cdot \left(v \cdot v\right)\right)}}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  5. Applied add-cube-cbrt0.0

    \[\leadsto \frac{\frac{\color{blue}{\left(\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}\right) \cdot \sqrt[3]{\frac{4}{3}}}}{1 \cdot \left(\pi - \pi \cdot \left(v \cdot v\right)\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  6. Applied times-frac0.0

    \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}}{1} \cdot \frac{\sqrt[3]{\frac{4}{3}}}{\pi - \pi \cdot \left(v \cdot v\right)}}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  7. Simplified0.0

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}\right)} \cdot \frac{\sqrt[3]{\frac{4}{3}}}{\pi - \pi \cdot \left(v \cdot v\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
  8. Using strategy rm

  9. Applied flip3--0.0

    \[\leadsto \frac{\left(\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}\right) \cdot \frac{\sqrt[3]{\frac{4}{3}}}{\color{blue}{\frac{{\pi}^{3} - {\left(\pi \cdot \left(v \cdot v\right)\right)}^{3}}{\pi \cdot \pi + \left(\left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right) + \pi \cdot \left(\pi \cdot \left(v \cdot v\right)\right)\right)}}}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  10. Applied associate-/r/0.0

    \[\leadsto \frac{\left(\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}\right) \cdot \color{blue}{\left(\frac{\sqrt[3]{\frac{4}{3}}}{{\pi}^{3} - {\left(\pi \cdot \left(v \cdot v\right)\right)}^{3}} \cdot \left(\pi \cdot \pi + \left(\left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right) + \pi \cdot \left(\pi \cdot \left(v \cdot v\right)\right)\right)\right)\right)}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  11. Simplified0.0

    \[\leadsto \frac{\left(\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}\right) \cdot \left(\color{blue}{\frac{\sqrt[3]{\frac{4}{3}}}{\pi \cdot \left(\pi \cdot \pi\right) - \left(\left(v \cdot \left(\pi \cdot v\right)\right) \cdot \left(v \cdot \left(\pi \cdot v\right)\right)\right) \cdot \left(v \cdot \left(\pi \cdot v\right)\right)}} \cdot \left(\pi \cdot \pi + \left(\left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right) + \pi \cdot \left(\pi \cdot \left(v \cdot v\right)\right)\right)\right)\right)}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

  12. Final simplification0.0

    \[\leadsto \frac{\left(\left(\left(\left(\pi \cdot \left(v \cdot v\right)\right) \cdot \left(\pi \cdot \left(v \cdot v\right)\right) + \left(\pi \cdot \left(v \cdot v\right)\right) \cdot \pi\right) + \pi \cdot \pi\right) \cdot \frac{\sqrt[3]{\frac{4}{3}}}{\pi \cdot \left(\pi \cdot \pi\right) - \left(\left(\left(\pi \cdot v\right) \cdot v\right) \cdot \left(\left(\pi \cdot v\right) \cdot v\right)\right) \cdot \left(\left(\pi \cdot v\right) \cdot v\right)}\right) \cdot \left(\sqrt[3]{\frac{4}{3}} \cdot \sqrt[3]{\frac{4}{3}}\right)}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]

Reproduce

herbie shell --seed 2019141 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))