Average Error: 1.0 → 0.0
Time: 19.2s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\sqrt[3]{\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)} \cdot \left(\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)}\right)}\]
\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)}}
↓
\sqrt[3]{\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)} \cdot \left(\frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)} \cdot \left(\left(\pi \cdot 3\right) \cdot \left(1 - v \cdot v\right)\right)}\right)}
double f(double v) {
        double r7363687 = 4.0;
        double r7363688 = 3.0;
        double r7363689 = atan2(1.0, 0.0);
        double r7363690 = r7363688 * r7363689;
        double r7363691 = 1.0;
        double r7363692 = v;
        double r7363693 = r7363692 * r7363692;
        double r7363694 = r7363691 - r7363693;
        double r7363695 = r7363690 * r7363694;
        double r7363696 = 2.0;
        double r7363697 = 6.0;
        double r7363698 = r7363697 * r7363693;
        double r7363699 = r7363696 - r7363698;
        double r7363700 = sqrt(r7363699);
        double r7363701 = r7363695 * r7363700;
        double r7363702 = r7363687 / r7363701;
        return r7363702;
}
↓
double f(double v) {
        double r7363703 = 4.0;
        double r7363704 = 2.0;
        double r7363705 = 6.0;
        double r7363706 = v;
        double r7363707 = r7363706 * r7363706;
        double r7363708 = r7363705 * r7363707;
        double r7363709 = r7363704 - r7363708;
        double r7363710 = sqrt(r7363709);
        double r7363711 = atan2(1.0, 0.0);
        double r7363712 = 3.0;
        double r7363713 = r7363711 * r7363712;
        double r7363714 = 1.0;
        double r7363715 = r7363714 - r7363707;
        double r7363716 = r7363713 * r7363715;
        double r7363717 = r7363710 * r7363716;
        double r7363718 = r7363703 / r7363717;
        double r7363719 = r7363718 * r7363718;
        double r7363720 = r7363718 * r7363719;
        double r7363721 = cbrt(r7363720);
        return r7363721;
}

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. Using strategy rm

  3. Applied add-cbrt-cube0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019192 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4.0 (* (* (* 3.0 PI) (- 1.0 (* v v))) (sqrt (- 2.0 (* 6.0 (* v v)))))))