Average Error: 0.0 → 0.0
Time: 25.4s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}} \cdot \left(\sqrt{\sqrt{1 - \sqrt[3]{\left(\left(\left(v \cdot v\right) \cdot 3\right) \cdot \left(\left(v \cdot v\right) \cdot 3\right)\right) \cdot \left(\left(v \cdot v\right) \cdot 3\right)}}} \cdot \frac{\sqrt{2}}{4}\right)\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\sqrt{\sqrt{1 - \left(v \cdot v\right) \cdot 3}} \cdot \left(\sqrt{\sqrt{1 - \sqrt[3]{\left(\left(\left(v \cdot v\right) \cdot 3\right) \cdot \left(\left(v \cdot v\right) \cdot 3\right)\right) \cdot \left(\left(v \cdot v\right) \cdot 3\right)}}} \cdot \frac{\sqrt{2}}{4}\right)\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r61989848 = 2.0;
        double r61989849 = sqrt(r61989848);
        double r61989850 = 4.0;
        double r61989851 = r61989849 / r61989850;
        double r61989852 = 1.0;
        double r61989853 = 3.0;
        double r61989854 = v;
        double r61989855 = r61989854 * r61989854;
        double r61989856 = r61989853 * r61989855;
        double r61989857 = r61989852 - r61989856;
        double r61989858 = sqrt(r61989857);
        double r61989859 = r61989851 * r61989858;
        double r61989860 = r61989852 - r61989855;
        double r61989861 = r61989859 * r61989860;
        return r61989861;
}
↓
double f(double v) {
        double r61989862 = 1.0;
        double r61989863 = v;
        double r61989864 = r61989863 * r61989863;
        double r61989865 = 3.0;
        double r61989866 = r61989864 * r61989865;
        double r61989867 = r61989862 - r61989866;
        double r61989868 = sqrt(r61989867);
        double r61989869 = sqrt(r61989868);
        double r61989870 = r61989866 * r61989866;
        double r61989871 = r61989870 * r61989866;
        double r61989872 = cbrt(r61989871);
        double r61989873 = r61989862 - r61989872;
        double r61989874 = sqrt(r61989873);
        double r61989875 = sqrt(r61989874);
        double r61989876 = 2.0;
        double r61989877 = sqrt(r61989876);
        double r61989878 = 4.0;
        double r61989879 = r61989877 / r61989878;
        double r61989880 = r61989875 * r61989879;
        double r61989881 = r61989869 * r61989880;
        double r61989882 = r61989862 - r61989864;
        double r61989883 = r61989881 * r61989882;
        return r61989883;
}

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-sqr-sqrt0.0

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

  4. Applied sqrt-prod0.0

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

  5. Applied associate-*r*0.0

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

  7. Applied add-cbrt-cube0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019107 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))