Average Error: 0.0 → 0.0
Time: 25.8s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\sqrt[3]{\left(\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right)} \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\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)
double f(double v) {
        double r10350778 = 2.0;
        double r10350779 = sqrt(r10350778);
        double r10350780 = 4.0;
        double r10350781 = r10350779 / r10350780;
        double r10350782 = 1.0;
        double r10350783 = 3.0;
        double r10350784 = v;
        double r10350785 = r10350784 * r10350784;
        double r10350786 = r10350783 * r10350785;
        double r10350787 = r10350782 - r10350786;
        double r10350788 = sqrt(r10350787);
        double r10350789 = r10350781 * r10350788;
        double r10350790 = r10350782 - r10350785;
        double r10350791 = r10350789 * r10350790;
        return r10350791;
}
↓
double f(double v) {
        double r10350792 = 2.0;
        double r10350793 = sqrt(r10350792);
        double r10350794 = 4.0;
        double r10350795 = r10350793 / r10350794;
        double r10350796 = 1.0;
        double r10350797 = 3.0;
        double r10350798 = v;
        double r10350799 = r10350798 * r10350798;
        double r10350800 = r10350797 * r10350799;
        double r10350801 = r10350796 - r10350800;
        double r10350802 = sqrt(r10350801);
        double r10350803 = r10350795 * r10350802;
        double r10350804 = r10350803 * r10350803;
        double r10350805 = r10350804 * r10350803;
        double r10350806 = cbrt(r10350805);
        double r10350807 = r10350796 - r10350799;
        double r10350808 = r10350806 * r10350807;
        return r10350808;
}

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

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

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))))