Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r257776 = 2.0;
        double r257777 = sqrt(r257776);
        double r257778 = 4.0;
        double r257779 = r257777 / r257778;
        double r257780 = 1.0;
        double r257781 = 3.0;
        double r257782 = v;
        double r257783 = r257782 * r257782;
        double r257784 = r257781 * r257783;
        double r257785 = r257780 - r257784;
        double r257786 = sqrt(r257785);
        double r257787 = r257779 * r257786;
        double r257788 = r257780 - r257783;
        double r257789 = r257787 * r257788;
        return r257789;
}
↓
double f(double v) {
        double r257790 = 2.0;
        double r257791 = sqrt(r257790);
        double r257792 = 4.0;
        double r257793 = r257791 / r257792;
        double r257794 = 1.0;
        double r257795 = 3.0;
        double r257796 = v;
        double r257797 = r257796 * r257796;
        double r257798 = r257795 * r257797;
        double r257799 = r257794 - r257798;
        double r257800 = sqrt(r257799);
        double r257801 = r257793 * r257800;
        double r257802 = r257794 - r257797;
        double r257803 = r257801 * r257802;
        return r257803;
}

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

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))