Average Error: 0.0 → 0.0
Time: 49.8s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \left(\log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right) \cdot \frac{\sqrt{2}}{4}\right)\]
\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 \left(\log \left(e^{\sqrt{1 - \left(v \cdot v\right) \cdot 3}}\right) \cdot \frac{\sqrt{2}}{4}\right)
double f(double v) {
        double r7129163 = 2.0;
        double r7129164 = sqrt(r7129163);
        double r7129165 = 4.0;
        double r7129166 = r7129164 / r7129165;
        double r7129167 = 1.0;
        double r7129168 = 3.0;
        double r7129169 = v;
        double r7129170 = r7129169 * r7129169;
        double r7129171 = r7129168 * r7129170;
        double r7129172 = r7129167 - r7129171;
        double r7129173 = sqrt(r7129172);
        double r7129174 = r7129166 * r7129173;
        double r7129175 = r7129167 - r7129170;
        double r7129176 = r7129174 * r7129175;
        return r7129176;
}
↓
double f(double v) {
        double r7129177 = 1.0;
        double r7129178 = v;
        double r7129179 = r7129178 * r7129178;
        double r7129180 = r7129177 - r7129179;
        double r7129181 = 3.0;
        double r7129182 = r7129179 * r7129181;
        double r7129183 = r7129177 - r7129182;
        double r7129184 = sqrt(r7129183);
        double r7129185 = exp(r7129184);
        double r7129186 = log(r7129185);
        double r7129187 = 2.0;
        double r7129188 = sqrt(r7129187);
        double r7129189 = 4.0;
        double r7129190 = r7129188 / r7129189;
        double r7129191 = r7129186 * r7129190;
        double r7129192 = r7129180 * r7129191;
        return r7129192;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))