Average Error: 1.0 → 0.0
Time: 6.9s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{3 \cdot \pi} \cdot \left(\frac{\sqrt[3]{1}}{1 - v \cdot v} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right)\]
\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)}}
↓
\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{3 \cdot \pi} \cdot \left(\frac{\sqrt[3]{1}}{1 - v \cdot v} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\right)
double f(double v) {
        double r256748 = 4.0;
        double r256749 = 3.0;
        double r256750 = atan2(1.0, 0.0);
        double r256751 = r256749 * r256750;
        double r256752 = 1.0;
        double r256753 = v;
        double r256754 = r256753 * r256753;
        double r256755 = r256752 - r256754;
        double r256756 = r256751 * r256755;
        double r256757 = 2.0;
        double r256758 = 6.0;
        double r256759 = r256758 * r256754;
        double r256760 = r256757 - r256759;
        double r256761 = sqrt(r256760);
        double r256762 = r256756 * r256761;
        double r256763 = r256748 / r256762;
        return r256763;
}
↓
double f(double v) {
        double r256764 = 1.0;
        double r256765 = cbrt(r256764);
        double r256766 = r256765 * r256765;
        double r256767 = 3.0;
        double r256768 = atan2(1.0, 0.0);
        double r256769 = r256767 * r256768;
        double r256770 = r256766 / r256769;
        double r256771 = 1.0;
        double r256772 = v;
        double r256773 = r256772 * r256772;
        double r256774 = r256771 - r256773;
        double r256775 = r256765 / r256774;
        double r256776 = 4.0;
        double r256777 = 2.0;
        double r256778 = 6.0;
        double r256779 = r256778 * r256773;
        double r256780 = r256777 - r256779;
        double r256781 = sqrt(r256780);
        double r256782 = r256776 / r256781;
        double r256783 = r256775 * r256782;
        double r256784 = r256770 * r256783;
        return r256784;
}

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 *-un-lft-identity1.0

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

  4. Applied times-frac0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied times-frac0.0

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

  8. Applied associate-*l*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))