Average Error: 1.0 → 0.0
Time: 6.0s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{1}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{4}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{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)}}
double f(double v) {
        double r312703 = 4.0;
        double r312704 = 3.0;
        double r312705 = atan2(1.0, 0.0);
        double r312706 = r312704 * r312705;
        double r312707 = 1.0;
        double r312708 = v;
        double r312709 = r312708 * r312708;
        double r312710 = r312707 - r312709;
        double r312711 = r312706 * r312710;
        double r312712 = 2.0;
        double r312713 = 6.0;
        double r312714 = r312713 * r312709;
        double r312715 = r312712 - r312714;
        double r312716 = sqrt(r312715);
        double r312717 = r312711 * r312716;
        double r312718 = r312703 / r312717;
        return r312718;
}
↓
double f(double v) {
        double r312719 = 1.0;
        double r312720 = 3.0;
        double r312721 = atan2(1.0, 0.0);
        double r312722 = r312720 * r312721;
        double r312723 = 1.0;
        double r312724 = v;
        double r312725 = r312724 * r312724;
        double r312726 = r312723 - r312725;
        double r312727 = r312722 * r312726;
        double r312728 = r312719 / r312727;
        double r312729 = 4.0;
        double r312730 = 2.0;
        double r312731 = 6.0;
        double r312732 = r312731 * r312725;
        double r312733 = r312730 - r312732;
        double r312734 = sqrt(r312733);
        double r312735 = r312729 / r312734;
        double r312736 = r312728 * r312735;
        return r312736;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))