Average Error: 0.0 → 0.0
Time: 14.0s
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 r2993672 = 2.0;
        double r2993673 = sqrt(r2993672);
        double r2993674 = 4.0;
        double r2993675 = r2993673 / r2993674;
        double r2993676 = 1.0;
        double r2993677 = 3.0;
        double r2993678 = v;
        double r2993679 = r2993678 * r2993678;
        double r2993680 = r2993677 * r2993679;
        double r2993681 = r2993676 - r2993680;
        double r2993682 = sqrt(r2993681);
        double r2993683 = r2993675 * r2993682;
        double r2993684 = r2993676 - r2993679;
        double r2993685 = r2993683 * r2993684;
        return r2993685;
}
↓
double f(double v) {
        double r2993686 = 1.0;
        double r2993687 = v;
        double r2993688 = r2993687 * r2993687;
        double r2993689 = 3.0;
        double r2993690 = r2993688 * r2993689;
        double r2993691 = r2993686 - r2993690;
        double r2993692 = sqrt(r2993691);
        double r2993693 = 2.0;
        double r2993694 = sqrt(r2993693);
        double r2993695 = 4.0;
        double r2993696 = r2993694 / r2993695;
        double r2993697 = r2993692 * r2993696;
        double r2993698 = r2993686 - r2993688;
        double r2993699 = r2993697 * r2993698;
        return r2993699;
}

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 2019153 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))