Average Error: 0.0 → 0.0
Time: 10.5s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)\]
\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{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r2394850 = 2.0;
        double r2394851 = sqrt(r2394850);
        double r2394852 = 4.0;
        double r2394853 = r2394851 / r2394852;
        double r2394854 = 1.0;
        double r2394855 = 3.0;
        double r2394856 = v;
        double r2394857 = r2394856 * r2394856;
        double r2394858 = r2394855 * r2394857;
        double r2394859 = r2394854 - r2394858;
        double r2394860 = sqrt(r2394859);
        double r2394861 = r2394853 * r2394860;
        double r2394862 = r2394854 - r2394857;
        double r2394863 = r2394861 * r2394862;
        return r2394863;
}
↓
double f(double v) {
        double r2394864 = 1.0;
        double r2394865 = v;
        double r2394866 = r2394865 * r2394865;
        double r2394867 = 3.0;
        double r2394868 = r2394866 * r2394867;
        double r2394869 = r2394864 - r2394868;
        double r2394870 = sqrt(r2394869);
        double r2394871 = 2.0;
        double r2394872 = sqrt(r2394871);
        double r2394873 = 4.0;
        double r2394874 = r2394872 / r2394873;
        double r2394875 = r2394870 * r2394874;
        double r2394876 = r2394864 - r2394866;
        double r2394877 = r2394875 * r2394876;
        return r2394877;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))