Average Error: 0.0 → 0.0
Time: 15.6s
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(1 - v \cdot v\right) \cdot \sqrt[3]{\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right)\right)}\]
\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 \sqrt[3]{\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right) \cdot \left(\sqrt{1 - \left(v \cdot v\right) \cdot 3} \cdot \frac{\sqrt{2}}{4}\right)\right)}
double f(double v) {
        double r6302118 = 2.0;
        double r6302119 = sqrt(r6302118);
        double r6302120 = 4.0;
        double r6302121 = r6302119 / r6302120;
        double r6302122 = 1.0;
        double r6302123 = 3.0;
        double r6302124 = v;
        double r6302125 = r6302124 * r6302124;
        double r6302126 = r6302123 * r6302125;
        double r6302127 = r6302122 - r6302126;
        double r6302128 = sqrt(r6302127);
        double r6302129 = r6302121 * r6302128;
        double r6302130 = r6302122 - r6302125;
        double r6302131 = r6302129 * r6302130;
        return r6302131;
}
↓
double f(double v) {
        double r6302132 = 1.0;
        double r6302133 = v;
        double r6302134 = r6302133 * r6302133;
        double r6302135 = r6302132 - r6302134;
        double r6302136 = 3.0;
        double r6302137 = r6302134 * r6302136;
        double r6302138 = r6302132 - r6302137;
        double r6302139 = sqrt(r6302138);
        double r6302140 = 2.0;
        double r6302141 = sqrt(r6302140);
        double r6302142 = 4.0;
        double r6302143 = r6302141 / r6302142;
        double r6302144 = r6302139 * r6302143;
        double r6302145 = r6302144 * r6302144;
        double r6302146 = r6302144 * r6302145;
        double r6302147 = cbrt(r6302146);
        double r6302148 = r6302135 * r6302147;
        return r6302148;
}

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-cbrt-cube0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019144 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))