Average Error: 1.0 → 0.0
Time: 7.3m
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{1}{\frac{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}{\frac{\frac{4}{3}}{\pi - \sqrt{\pi \cdot \left(v \cdot v\right)} \cdot \sqrt{\pi \cdot \left(v \cdot v\right)}}}}\]
\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{1}{\frac{\sqrt{2 + \left(v \cdot -6\right) \cdot v}}{\frac{\frac{4}{3}}{\pi - \sqrt{\pi \cdot \left(v \cdot v\right)} \cdot \sqrt{\pi \cdot \left(v \cdot v\right)}}}}
double f(double v) {
        double r48289748 = 4.0;
        double r48289749 = 3.0;
        double r48289750 = atan2(1.0, 0.0);
        double r48289751 = r48289749 * r48289750;
        double r48289752 = 1.0;
        double r48289753 = v;
        double r48289754 = r48289753 * r48289753;
        double r48289755 = r48289752 - r48289754;
        double r48289756 = r48289751 * r48289755;
        double r48289757 = 2.0;
        double r48289758 = 6.0;
        double r48289759 = r48289758 * r48289754;
        double r48289760 = r48289757 - r48289759;
        double r48289761 = sqrt(r48289760);
        double r48289762 = r48289756 * r48289761;
        double r48289763 = r48289748 / r48289762;
        return r48289763;
}
↓
double f(double v) {
        double r48289764 = 1.0;
        double r48289765 = 2.0;
        double r48289766 = v;
        double r48289767 = -6.0;
        double r48289768 = r48289766 * r48289767;
        double r48289769 = r48289768 * r48289766;
        double r48289770 = r48289765 + r48289769;
        double r48289771 = sqrt(r48289770);
        double r48289772 = 1.3333333333333333;
        double r48289773 = atan2(1.0, 0.0);
        double r48289774 = r48289766 * r48289766;
        double r48289775 = r48289773 * r48289774;
        double r48289776 = sqrt(r48289775);
        double r48289777 = r48289776 * r48289776;
        double r48289778 = r48289773 - r48289777;
        double r48289779 = r48289772 / r48289778;
        double r48289780 = r48289771 / r48289779;
        double r48289781 = r48289764 / r48289780;
        return r48289781;
}

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

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

  4. Applied clear-num0.0

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

  6. Applied add-sqr-sqrt0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019107 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))