Average Error: 1.0 → 0.0
Time: 6.8s
Precision: 64
\[\frac{4}{\left(\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)\right) \cdot \sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
↓
\[\frac{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}\]
\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{\sqrt{4}}{\left(3 \cdot \pi\right) \cdot \left(1 - v \cdot v\right)} \cdot \frac{\sqrt{4}}{\sqrt{2 - 6 \cdot \left(v \cdot v\right)}}
double f(double v) {
        double r304720 = 4.0;
        double r304721 = 3.0;
        double r304722 = atan2(1.0, 0.0);
        double r304723 = r304721 * r304722;
        double r304724 = 1.0;
        double r304725 = v;
        double r304726 = r304725 * r304725;
        double r304727 = r304724 - r304726;
        double r304728 = r304723 * r304727;
        double r304729 = 2.0;
        double r304730 = 6.0;
        double r304731 = r304730 * r304726;
        double r304732 = r304729 - r304731;
        double r304733 = sqrt(r304732);
        double r304734 = r304728 * r304733;
        double r304735 = r304720 / r304734;
        return r304735;
}
↓
double f(double v) {
        double r304736 = 4.0;
        double r304737 = sqrt(r304736);
        double r304738 = 3.0;
        double r304739 = atan2(1.0, 0.0);
        double r304740 = r304738 * r304739;
        double r304741 = 1.0;
        double r304742 = v;
        double r304743 = r304742 * r304742;
        double r304744 = r304741 - r304743;
        double r304745 = r304740 * r304744;
        double r304746 = r304737 / r304745;
        double r304747 = 2.0;
        double r304748 = 6.0;
        double r304749 = r304748 * r304743;
        double r304750 = r304747 - r304749;
        double r304751 = sqrt(r304750);
        double r304752 = r304737 / r304751;
        double r304753 = r304746 * r304752;
        return r304753;
}

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-sqr-sqrt1.0

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

  4. Applied times-frac0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 
(FPCore (v)
  :name "Falkner and Boettcher, Equation (22+)"
  :precision binary64
  (/ 4 (* (* (* 3 PI) (- 1 (* v v))) (sqrt (- 2 (* 6 (* v v)))))))