Average Error: 0.0 → 0.0
Time: 14.3s
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 r3914697 = 2.0;
        double r3914698 = sqrt(r3914697);
        double r3914699 = 4.0;
        double r3914700 = r3914698 / r3914699;
        double r3914701 = 1.0;
        double r3914702 = 3.0;
        double r3914703 = v;
        double r3914704 = r3914703 * r3914703;
        double r3914705 = r3914702 * r3914704;
        double r3914706 = r3914701 - r3914705;
        double r3914707 = sqrt(r3914706);
        double r3914708 = r3914700 * r3914707;
        double r3914709 = r3914701 - r3914704;
        double r3914710 = r3914708 * r3914709;
        return r3914710;
}
↓
double f(double v) {
        double r3914711 = 1.0;
        double r3914712 = v;
        double r3914713 = r3914712 * r3914712;
        double r3914714 = r3914711 - r3914713;
        double r3914715 = 3.0;
        double r3914716 = r3914713 * r3914715;
        double r3914717 = r3914711 - r3914716;
        double r3914718 = sqrt(r3914717);
        double r3914719 = 2.0;
        double r3914720 = sqrt(r3914719);
        double r3914721 = 4.0;
        double r3914722 = r3914720 / r3914721;
        double r3914723 = r3914718 * r3914722;
        double r3914724 = exp(r3914723);
        double r3914725 = log(r3914724);
        double r3914726 = r3914714 * r3914725;
        return r3914726;
}

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 2019152 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))