Average Error: 0.0 → 0.0
Time: 14.0s
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 r5943938 = 2.0;
        double r5943939 = sqrt(r5943938);
        double r5943940 = 4.0;
        double r5943941 = r5943939 / r5943940;
        double r5943942 = 1.0;
        double r5943943 = 3.0;
        double r5943944 = v;
        double r5943945 = r5943944 * r5943944;
        double r5943946 = r5943943 * r5943945;
        double r5943947 = r5943942 - r5943946;
        double r5943948 = sqrt(r5943947);
        double r5943949 = r5943941 * r5943948;
        double r5943950 = r5943942 - r5943945;
        double r5943951 = r5943949 * r5943950;
        return r5943951;
}
↓
double f(double v) {
        double r5943952 = 1.0;
        double r5943953 = v;
        double r5943954 = r5943953 * r5943953;
        double r5943955 = 3.0;
        double r5943956 = r5943954 * r5943955;
        double r5943957 = r5943952 - r5943956;
        double r5943958 = sqrt(r5943957);
        double r5943959 = 2.0;
        double r5943960 = sqrt(r5943959);
        double r5943961 = 4.0;
        double r5943962 = r5943960 / r5943961;
        double r5943963 = r5943958 * r5943962;
        double r5943964 = r5943952 - r5943954;
        double r5943965 = r5943963 * r5943964;
        return r5943965;
}

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 2019138 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))