Average Error: 0.0 → 0.0
Time: 22.6s
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 r245619 = 2.0;
        double r245620 = sqrt(r245619);
        double r245621 = 4.0;
        double r245622 = r245620 / r245621;
        double r245623 = 1.0;
        double r245624 = 3.0;
        double r245625 = v;
        double r245626 = r245625 * r245625;
        double r245627 = r245624 * r245626;
        double r245628 = r245623 - r245627;
        double r245629 = sqrt(r245628);
        double r245630 = r245622 * r245629;
        double r245631 = r245623 - r245626;
        double r245632 = r245630 * r245631;
        return r245632;
}
↓
double f(double v) {
        double r245633 = 1.0;
        double r245634 = v;
        double r245635 = r245634 * r245634;
        double r245636 = 3.0;
        double r245637 = r245635 * r245636;
        double r245638 = r245633 - r245637;
        double r245639 = sqrt(r245638);
        double r245640 = 2.0;
        double r245641 = sqrt(r245640);
        double r245642 = 4.0;
        double r245643 = r245641 / r245642;
        double r245644 = r245639 * r245643;
        double r245645 = r245633 - r245635;
        double r245646 = r245644 * r245645;
        return r245646;
}

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 2019194 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2.0) 4.0) (sqrt (- 1.0 (* 3.0 (* v v))))) (- 1.0 (* v v))))