Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\log \left(e^{\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}}\right) \cdot \left(1 - v \cdot v\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\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)
double f(double v) {
        double r384981 = 2.0;
        double r384982 = sqrt(r384981);
        double r384983 = 4.0;
        double r384984 = r384982 / r384983;
        double r384985 = 1.0;
        double r384986 = 3.0;
        double r384987 = v;
        double r384988 = r384987 * r384987;
        double r384989 = r384986 * r384988;
        double r384990 = r384985 - r384989;
        double r384991 = sqrt(r384990);
        double r384992 = r384984 * r384991;
        double r384993 = r384985 - r384988;
        double r384994 = r384992 * r384993;
        return r384994;
}
↓
double f(double v) {
        double r384995 = 2.0;
        double r384996 = sqrt(r384995);
        double r384997 = 4.0;
        double r384998 = r384996 / r384997;
        double r384999 = 1.0;
        double r385000 = 3.0;
        double r385001 = v;
        double r385002 = r385001 * r385001;
        double r385003 = r385000 * r385002;
        double r385004 = r384999 - r385003;
        double r385005 = sqrt(r385004);
        double r385006 = r384998 * r385005;
        double r385007 = exp(r385006);
        double r385008 = log(r385007);
        double r385009 = r384999 - r385002;
        double r385010 = r385008 * r385009;
        return r385010;
}

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

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  :precision binary64
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))