Average Error: 0.0 → 0.0
Time: 9.7s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \log \left(e^{3 \cdot \left(v \cdot v\right)}\right)}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - \log \left(e^{3 \cdot \left(v \cdot v\right)}\right)}\right) \cdot \left(1 - v \cdot v\right)
double f(double v) {
        double r208826 = 2.0;
        double r208827 = sqrt(r208826);
        double r208828 = 4.0;
        double r208829 = r208827 / r208828;
        double r208830 = 1.0;
        double r208831 = 3.0;
        double r208832 = v;
        double r208833 = r208832 * r208832;
        double r208834 = r208831 * r208833;
        double r208835 = r208830 - r208834;
        double r208836 = sqrt(r208835);
        double r208837 = r208829 * r208836;
        double r208838 = r208830 - r208833;
        double r208839 = r208837 * r208838;
        return r208839;
}
↓
double f(double v) {
        double r208840 = 2.0;
        double r208841 = sqrt(r208840);
        double r208842 = 4.0;
        double r208843 = r208841 / r208842;
        double r208844 = 1.0;
        double r208845 = 3.0;
        double r208846 = v;
        double r208847 = r208846 * r208846;
        double r208848 = r208845 * r208847;
        double r208849 = exp(r208848);
        double r208850 = log(r208849);
        double r208851 = r208844 - r208850;
        double r208852 = sqrt(r208851);
        double r208853 = r208843 * r208852;
        double r208854 = r208844 - r208847;
        double r208855 = r208853 * r208854;
        return r208855;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))