Average Error: 0.0 → 0.0
Time: 12.1s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}}\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(1 - v \cdot v\right) \cdot \log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}}\right)
double f(double v) {
        double r8209689 = 2.0;
        double r8209690 = sqrt(r8209689);
        double r8209691 = 4.0;
        double r8209692 = r8209690 / r8209691;
        double r8209693 = 1.0;
        double r8209694 = 3.0;
        double r8209695 = v;
        double r8209696 = r8209695 * r8209695;
        double r8209697 = r8209694 * r8209696;
        double r8209698 = r8209693 - r8209697;
        double r8209699 = sqrt(r8209698);
        double r8209700 = r8209692 * r8209699;
        double r8209701 = r8209693 - r8209696;
        double r8209702 = r8209700 * r8209701;
        return r8209702;
}
↓
double f(double v) {
        double r8209703 = 1.0;
        double r8209704 = v;
        double r8209705 = r8209704 * r8209704;
        double r8209706 = r8209703 - r8209705;
        double r8209707 = 3.0;
        double r8209708 = r8209705 * r8209707;
        double r8209709 = r8209703 - r8209708;
        double r8209710 = sqrt(r8209709);
        double r8209711 = 2.0;
        double r8209712 = sqrt(r8209711);
        double r8209713 = 4.0;
        double r8209714 = r8209712 / r8209713;
        double r8209715 = r8209710 * r8209714;
        double r8209716 = exp(r8209715);
        double r8209717 = log(r8209716);
        double r8209718 = r8209706 * r8209717;
        return r8209718;
}

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 add-log-exp0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(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))))