Average Error: 0.0 → 0.0
Time: 24.6s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(-v \cdot v\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\right) + \frac{\sqrt{2}}{4} \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(-v \cdot v\right) \cdot \left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\right) + \frac{\sqrt{2}}{4} \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}
double f(double v) {
        double r6216696 = 2.0;
        double r6216697 = sqrt(r6216696);
        double r6216698 = 4.0;
        double r6216699 = r6216697 / r6216698;
        double r6216700 = 1.0;
        double r6216701 = 3.0;
        double r6216702 = v;
        double r6216703 = r6216702 * r6216702;
        double r6216704 = r6216701 * r6216703;
        double r6216705 = r6216700 - r6216704;
        double r6216706 = sqrt(r6216705);
        double r6216707 = r6216699 * r6216706;
        double r6216708 = r6216700 - r6216703;
        double r6216709 = r6216707 * r6216708;
        return r6216709;
}
↓
double f(double v) {
        double r6216710 = v;
        double r6216711 = r6216710 * r6216710;
        double r6216712 = -r6216711;
        double r6216713 = 2.0;
        double r6216714 = sqrt(r6216713);
        double r6216715 = 4.0;
        double r6216716 = r6216714 / r6216715;
        double r6216717 = 1.0;
        double r6216718 = 3.0;
        double r6216719 = r6216711 * r6216718;
        double r6216720 = r6216717 - r6216719;
        double r6216721 = sqrt(r6216720);
        double r6216722 = r6216716 * r6216721;
        double r6216723 = r6216712 * r6216722;
        double r6216724 = r6216723 + r6216722;
        return r6216724;
}

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. Using strategy rm

  3. Applied sub-neg0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019143 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))