Average Error: 0.0 → 0.0
Time: 14.9s
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 r4775067 = 2.0;
        double r4775068 = sqrt(r4775067);
        double r4775069 = 4.0;
        double r4775070 = r4775068 / r4775069;
        double r4775071 = 1.0;
        double r4775072 = 3.0;
        double r4775073 = v;
        double r4775074 = r4775073 * r4775073;
        double r4775075 = r4775072 * r4775074;
        double r4775076 = r4775071 - r4775075;
        double r4775077 = sqrt(r4775076);
        double r4775078 = r4775070 * r4775077;
        double r4775079 = r4775071 - r4775074;
        double r4775080 = r4775078 * r4775079;
        return r4775080;
}
↓
double f(double v) {
        double r4775081 = 1.0;
        double r4775082 = v;
        double r4775083 = r4775082 * r4775082;
        double r4775084 = 3.0;
        double r4775085 = r4775083 * r4775084;
        double r4775086 = r4775081 - r4775085;
        double r4775087 = sqrt(r4775086);
        double r4775088 = 2.0;
        double r4775089 = sqrt(r4775088);
        double r4775090 = 4.0;
        double r4775091 = r4775089 / r4775090;
        double r4775092 = r4775087 * r4775091;
        double r4775093 = r4775081 - r4775083;
        double r4775094 = r4775092 * r4775093;
        return r4775094;
}

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 2019135 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))