Average Error: 0.0 → 0.0
Time: 17.5s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\left(\sqrt{1 - v \cdot v} \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\right) \cdot \sqrt{1 - v \cdot v}\right) \cdot \frac{\sqrt{2}}{4}\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\left(\sqrt{1 - v \cdot v} \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\right) \cdot \sqrt{1 - v \cdot v}\right) \cdot \frac{\sqrt{2}}{4}
double f(double v) {
        double r7571167 = 2.0;
        double r7571168 = sqrt(r7571167);
        double r7571169 = 4.0;
        double r7571170 = r7571168 / r7571169;
        double r7571171 = 1.0;
        double r7571172 = 3.0;
        double r7571173 = v;
        double r7571174 = r7571173 * r7571173;
        double r7571175 = r7571172 * r7571174;
        double r7571176 = r7571171 - r7571175;
        double r7571177 = sqrt(r7571176);
        double r7571178 = r7571170 * r7571177;
        double r7571179 = r7571171 - r7571174;
        double r7571180 = r7571178 * r7571179;
        return r7571180;
}
↓
double f(double v) {
        double r7571181 = 1.0;
        double r7571182 = v;
        double r7571183 = r7571182 * r7571182;
        double r7571184 = r7571181 - r7571183;
        double r7571185 = sqrt(r7571184);
        double r7571186 = 3.0;
        double r7571187 = r7571183 * r7571186;
        double r7571188 = r7571181 - r7571187;
        double r7571189 = sqrt(r7571188);
        double r7571190 = r7571185 * r7571189;
        double r7571191 = r7571190 * r7571185;
        double r7571192 = 2.0;
        double r7571193 = sqrt(r7571192);
        double r7571194 = 4.0;
        double r7571195 = r7571193 / r7571194;
        double r7571196 = r7571191 * r7571195;
        return r7571196;
}

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 associate-*l*0.0

    \[\leadsto \color{blue}{\frac{\sqrt{2}}{4} \cdot \left(\sqrt{1 - 3 \cdot \left(v \cdot v\right)} \cdot \left(1 - v \cdot v\right)\right)}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.0

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

  6. Applied associate-*r*0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019139 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))