Average Error: 0.0 → 0.0
Time: 12.8s
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 r42370691 = 2.0;
        double r42370692 = sqrt(r42370691);
        double r42370693 = 4.0;
        double r42370694 = r42370692 / r42370693;
        double r42370695 = 1.0;
        double r42370696 = 3.0;
        double r42370697 = v;
        double r42370698 = r42370697 * r42370697;
        double r42370699 = r42370696 * r42370698;
        double r42370700 = r42370695 - r42370699;
        double r42370701 = sqrt(r42370700);
        double r42370702 = r42370694 * r42370701;
        double r42370703 = r42370695 - r42370698;
        double r42370704 = r42370702 * r42370703;
        return r42370704;
}
↓
double f(double v) {
        double r42370705 = 1.0;
        double r42370706 = v;
        double r42370707 = r42370706 * r42370706;
        double r42370708 = 3.0;
        double r42370709 = r42370707 * r42370708;
        double r42370710 = r42370705 - r42370709;
        double r42370711 = sqrt(r42370710);
        double r42370712 = 2.0;
        double r42370713 = sqrt(r42370712);
        double r42370714 = 4.0;
        double r42370715 = r42370713 / r42370714;
        double r42370716 = r42370711 * r42370715;
        double r42370717 = r42370705 - r42370707;
        double r42370718 = r42370716 * r42370717;
        return r42370718;
}

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