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 r58413128 = 2.0;
        double r58413129 = sqrt(r58413128);
        double r58413130 = 4.0;
        double r58413131 = r58413129 / r58413130;
        double r58413132 = 1.0;
        double r58413133 = 3.0;
        double r58413134 = v;
        double r58413135 = r58413134 * r58413134;
        double r58413136 = r58413133 * r58413135;
        double r58413137 = r58413132 - r58413136;
        double r58413138 = sqrt(r58413137);
        double r58413139 = r58413131 * r58413138;
        double r58413140 = r58413132 - r58413135;
        double r58413141 = r58413139 * r58413140;
        return r58413141;
}
↓
double f(double v) {
        double r58413142 = 1.0;
        double r58413143 = v;
        double r58413144 = r58413143 * r58413143;
        double r58413145 = 3.0;
        double r58413146 = r58413144 * r58413145;
        double r58413147 = r58413142 - r58413146;
        double r58413148 = sqrt(r58413147);
        double r58413149 = 2.0;
        double r58413150 = sqrt(r58413149);
        double r58413151 = 4.0;
        double r58413152 = r58413150 / r58413151;
        double r58413153 = r58413148 * r58413152;
        double r58413154 = r58413142 - r58413144;
        double r58413155 = r58413153 * r58413154;
        return r58413155;
}

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 2019121 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))