Average Error: 0.0 → 0.0
Time: 1.6m
Precision: 64
\[\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)\]
↓
\[\left(\left(\left(1 - v \cdot v\right) \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\right) \cdot \frac{\sqrt[3]{\sqrt{2}}}{4}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)\]
\left(\frac{\sqrt{2}}{4} \cdot \sqrt{1 - 3 \cdot \left(v \cdot v\right)}\right) \cdot \left(1 - v \cdot v\right)
↓
\left(\left(\left(1 - v \cdot v\right) \cdot \sqrt{1 - \left(v \cdot v\right) \cdot 3}\right) \cdot \frac{\sqrt[3]{\sqrt{2}}}{4}\right) \cdot \left(\sqrt[3]{\sqrt{2}} \cdot \sqrt[3]{\sqrt{2}}\right)
double f(double v) {
        double r43465132 = 2.0;
        double r43465133 = sqrt(r43465132);
        double r43465134 = 4.0;
        double r43465135 = r43465133 / r43465134;
        double r43465136 = 1.0;
        double r43465137 = 3.0;
        double r43465138 = v;
        double r43465139 = r43465138 * r43465138;
        double r43465140 = r43465137 * r43465139;
        double r43465141 = r43465136 - r43465140;
        double r43465142 = sqrt(r43465141);
        double r43465143 = r43465135 * r43465142;
        double r43465144 = r43465136 - r43465139;
        double r43465145 = r43465143 * r43465144;
        return r43465145;
}
↓
double f(double v) {
        double r43465146 = 1.0;
        double r43465147 = v;
        double r43465148 = r43465147 * r43465147;
        double r43465149 = r43465146 - r43465148;
        double r43465150 = 3.0;
        double r43465151 = r43465148 * r43465150;
        double r43465152 = r43465146 - r43465151;
        double r43465153 = sqrt(r43465152);
        double r43465154 = r43465149 * r43465153;
        double r43465155 = 2.0;
        double r43465156 = sqrt(r43465155);
        double r43465157 = cbrt(r43465156);
        double r43465158 = 4.0;
        double r43465159 = r43465157 / r43465158;
        double r43465160 = r43465154 * r43465159;
        double r43465161 = r43465157 * r43465157;
        double r43465162 = r43465160 * r43465161;
        return r43465162;
}

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 *-un-lft-identity0.0

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

  6. Applied add-cube-cbrt0.0

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

  7. Applied times-frac0.0

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

  8. Applied associate-*l*0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019104 
(FPCore (v)
  :name "Falkner and Boettcher, Appendix B, 2"
  (* (* (/ (sqrt 2) 4) (sqrt (- 1 (* 3 (* v v))))) (- 1 (* v v))))