Average Error: 15.9 → 1.3
Time: 5.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\frac{1}{\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\frac{1}{\sqrt[3]{\sqrt[3]{a} \cdot \sqrt[3]{a}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)
double f(double g, double a) {
        double r170233 = g;
        double r170234 = 2.0;
        double r170235 = a;
        double r170236 = r170234 * r170235;
        double r170237 = r170233 / r170236;
        double r170238 = cbrt(r170237);
        return r170238;
}
↓
double f(double g, double a) {
        double r170239 = g;
        double r170240 = cbrt(r170239);
        double r170241 = r170240 * r170240;
        double r170242 = 2.0;
        double r170243 = r170241 / r170242;
        double r170244 = cbrt(r170243);
        double r170245 = 1.0;
        double r170246 = a;
        double r170247 = cbrt(r170246);
        double r170248 = r170247 * r170247;
        double r170249 = cbrt(r170248);
        double r170250 = r170245 / r170249;
        double r170251 = r170240 / r170247;
        double r170252 = cbrt(r170251);
        double r170253 = r170250 * r170252;
        double r170254 = r170244 * r170253;
        return r170254;
}

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 15.9

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

  3. Applied add-cube-cbrt16.0

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

  4. Applied times-frac16.0

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

  5. Applied cbrt-prod6.0

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

  7. Applied add-cube-cbrt6.1

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

  8. Applied *-un-lft-identity6.1

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

  9. Applied cbrt-prod6.1

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

  10. Applied times-frac6.1

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

  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 cbrt-div1.3

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

  15. Simplified1.3

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

  16. Final simplification1.3

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

Reproduce

herbie shell --seed 2020003 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))