Average Error: 0.0 → 0.0
Time: 22.7s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \sqrt[3]{\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right)\right)}\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(1 - v \cdot v\right) \cdot \sqrt[3]{\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right)\right)}
double f(double v) {
        double r4658677 = 2.0;
        double r4658678 = sqrt(r4658677);
        double r4658679 = 4.0;
        double r4658680 = r4658678 / r4658679;
        double r4658681 = 1.0;
        double r4658682 = 3.0;
        double r4658683 = v;
        double r4658684 = r4658683 * r4658683;
        double r4658685 = r4658682 * r4658684;
        double r4658686 = r4658681 - r4658685;
        double r4658687 = sqrt(r4658686);
        double r4658688 = r4658680 * r4658687;
        double r4658689 = r4658681 - r4658684;
        double r4658690 = r4658688 * r4658689;
        return r4658690;
}
↓
double f(double v) {
        double r4658691 = 1.0;
        double r4658692 = v;
        double r4658693 = r4658692 * r4658692;
        double r4658694 = r4658691 - r4658693;
        double r4658695 = 3.0;
        double r4658696 = r4658693 * r4658695;
        double r4658697 = r4658691 - r4658696;
        double r4658698 = sqrt(r4658697);
        double r4658699 = 2.0;
        double r4658700 = sqrt(r4658699);
        double r4658701 = 4.0;
        double r4658702 = r4658700 / r4658701;
        double r4658703 = r4658698 * r4658702;
        double r4658704 = r4658703 * r4658703;
        double r4658705 = r4658703 * r4658704;
        double r4658706 = cbrt(r4658705);
        double r4658707 = r4658694 * r4658706;
        return r4658707;
}

Error

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))