Average Error: 0.0 → 0.0
Time: 13.2s
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 r5400903 = 2.0;
        double r5400904 = sqrt(r5400903);
        double r5400905 = 4.0;
        double r5400906 = r5400904 / r5400905;
        double r5400907 = 1.0;
        double r5400908 = 3.0;
        double r5400909 = v;
        double r5400910 = r5400909 * r5400909;
        double r5400911 = r5400908 * r5400910;
        double r5400912 = r5400907 - r5400911;
        double r5400913 = sqrt(r5400912);
        double r5400914 = r5400906 * r5400913;
        double r5400915 = r5400907 - r5400910;
        double r5400916 = r5400914 * r5400915;
        return r5400916;
}
↓
double f(double v) {
        double r5400917 = 1.0;
        double r5400918 = v;
        double r5400919 = r5400918 * r5400918;
        double r5400920 = 3.0;
        double r5400921 = r5400919 * r5400920;
        double r5400922 = r5400917 - r5400921;
        double r5400923 = sqrt(r5400922);
        double r5400924 = 2.0;
        double r5400925 = sqrt(r5400924);
        double r5400926 = 4.0;
        double r5400927 = r5400925 / r5400926;
        double r5400928 = r5400923 * r5400927;
        double r5400929 = r5400917 - r5400919;
        double r5400930 = r5400928 * r5400929;
        return r5400930;
}

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