Average Error: 15.6 → 1.3
Time: 6.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)
double f(double g, double a) {
        double r111305 = g;
        double r111306 = 2.0;
        double r111307 = a;
        double r111308 = r111306 * r111307;
        double r111309 = r111305 / r111308;
        double r111310 = cbrt(r111309);
        return r111310;
}
↓
double f(double g, double a) {
        double r111311 = g;
        double r111312 = cbrt(r111311);
        double r111313 = r111312 * r111312;
        double r111314 = 2.0;
        double r111315 = r111313 / r111314;
        double r111316 = cbrt(r111315);
        double r111317 = 1.0;
        double r111318 = a;
        double r111319 = cbrt(r111318);
        double r111320 = r111319 * r111319;
        double r111321 = cbrt(r111320);
        double r111322 = cbrt(r111319);
        double r111323 = r111321 * r111322;
        double r111324 = r111319 * r111323;
        double r111325 = r111317 / r111324;
        double r111326 = cbrt(r111325);
        double r111327 = r111312 / r111319;
        double r111328 = cbrt(r111327);
        double r111329 = r111326 * r111328;
        double r111330 = r111316 * r111329;
        return r111330;
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.6

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt15.8

    \[\leadsto \sqrt[3]{\frac{\color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{g}}}{2 \cdot a}}\]

  4. Applied times-frac15.8

    \[\leadsto \sqrt[3]{\color{blue}{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2} \cdot \frac{\sqrt[3]{g}}{a}}}\]

  5. Applied cbrt-prod5.8

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{a}}}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt5.9

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}}\]

  8. Applied *-un-lft-identity5.9

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\frac{\sqrt[3]{\color{blue}{1 \cdot g}}}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\]

  9. Applied cbrt-prod5.9

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\frac{\color{blue}{\sqrt[3]{1} \cdot \sqrt[3]{g}}}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}\]

  10. Applied times-frac5.9

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt[3]{1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \frac{\sqrt[3]{g}}{\sqrt[3]{a}}}}\]

  11. Applied cbrt-prod1.3

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \color{blue}{\left(\sqrt[3]{\frac{\sqrt[3]{1}}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)}\]

  12. Simplified1.3

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\color{blue}{\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]
  13. Using strategy rm

  14. Applied add-cube-cbrt1.3

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{a} \cdot \sqrt[3]{a}\right) \cdot \sqrt[3]{a}}}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]

  15. Applied cbrt-prod1.3

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \color{blue}{\left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]

  16. Final simplification1.3

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \left(\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}} \cdot \sqrt[3]{\sqrt[3]{a}}\right)}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))