Average Error: 0.0 → 0.0
Time: 20.2s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \left(1 - v \cdot v\right)\right) \cdot \frac{\sqrt{2}}{4}\]
\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 \left(1 - v \cdot v\right)\right) \cdot \frac{\sqrt{2}}{4}
double f(double v) {
        double r6920715 = 2.0;
        double r6920716 = sqrt(r6920715);
        double r6920717 = 4.0;
        double r6920718 = r6920716 / r6920717;
        double r6920719 = 1.0;
        double r6920720 = 3.0;
        double r6920721 = v;
        double r6920722 = r6920721 * r6920721;
        double r6920723 = r6920720 * r6920722;
        double r6920724 = r6920719 - r6920723;
        double r6920725 = sqrt(r6920724);
        double r6920726 = r6920718 * r6920725;
        double r6920727 = r6920719 - r6920722;
        double r6920728 = r6920726 * r6920727;
        return r6920728;
}
↓
double f(double v) {
        double r6920729 = 1.0;
        double r6920730 = v;
        double r6920731 = r6920730 * r6920730;
        double r6920732 = 3.0;
        double r6920733 = r6920731 * r6920732;
        double r6920734 = r6920729 - r6920733;
        double r6920735 = sqrt(r6920734);
        double r6920736 = r6920729 - r6920731;
        double r6920737 = r6920735 * r6920736;
        double r6920738 = 2.0;
        double r6920739 = sqrt(r6920738);
        double r6920740 = 4.0;
        double r6920741 = r6920739 / r6920740;
        double r6920742 = r6920737 * r6920741;
        return r6920742;
}

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. Using strategy rm

  3. Applied associate-*l*0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))