Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\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 r303705 = 2.0;
        double r303706 = sqrt(r303705);
        double r303707 = 4.0;
        double r303708 = r303706 / r303707;
        double r303709 = 1.0;
        double r303710 = 3.0;
        double r303711 = v;
        double r303712 = r303711 * r303711;
        double r303713 = r303710 * r303712;
        double r303714 = r303709 - r303713;
        double r303715 = sqrt(r303714);
        double r303716 = r303708 * r303715;
        double r303717 = r303709 - r303712;
        double r303718 = r303716 * r303717;
        return r303718;
}
↓
double f(double v) {
        double r303719 = 2.0;
        double r303720 = sqrt(r303719);
        double r303721 = 4.0;
        double r303722 = r303720 / r303721;
        double r303723 = 1.0;
        double r303724 = 3.0;
        double r303725 = v;
        double r303726 = r303725 * r303725;
        double r303727 = r303724 * r303726;
        double r303728 = r303723 - r303727;
        double r303729 = sqrt(r303728);
        double r303730 = r303722 * r303729;
        double r303731 = r303723 - r303726;
        double r303732 = r303730 * r303731;
        return r303732;
}

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 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))