Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\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 r196922 = 2.0;
        double r196923 = sqrt(r196922);
        double r196924 = 4.0;
        double r196925 = r196923 / r196924;
        double r196926 = 1.0;
        double r196927 = 3.0;
        double r196928 = v;
        double r196929 = r196928 * r196928;
        double r196930 = r196927 * r196929;
        double r196931 = r196926 - r196930;
        double r196932 = sqrt(r196931);
        double r196933 = r196925 * r196932;
        double r196934 = r196926 - r196929;
        double r196935 = r196933 * r196934;
        return r196935;
}
↓
double f(double v) {
        double r196936 = 2.0;
        double r196937 = sqrt(r196936);
        double r196938 = 4.0;
        double r196939 = r196937 / r196938;
        double r196940 = 1.0;
        double r196941 = 3.0;
        double r196942 = v;
        double r196943 = r196942 * r196942;
        double r196944 = r196941 * r196943;
        double r196945 = r196940 - r196944;
        double r196946 = sqrt(r196945);
        double r196947 = r196939 * r196946;
        double r196948 = r196940 - r196943;
        double r196949 = r196947 * r196948;
        return r196949;
}

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

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

Reproduce

herbie shell --seed 2020060 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))