Average Error: 15.8 → 1.3
Time: 5.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\left(\sqrt[3]{\sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right) \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{\left(\sqrt[3]{\sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right) \cdot \sqrt[3]{\sqrt[3]{g}}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r167987 = g;
        double r167988 = 2.0;
        double r167989 = a;
        double r167990 = r167988 * r167989;
        double r167991 = r167987 / r167990;
        double r167992 = cbrt(r167991);
        return r167992;
}
↓
double f(double g, double a) {
        double r167993 = g;
        double r167994 = cbrt(r167993);
        double r167995 = r167994 * r167994;
        double r167996 = 2.0;
        double r167997 = r167995 / r167996;
        double r167998 = cbrt(r167997);
        double r167999 = cbrt(r167994);
        double r168000 = r167999 * r167999;
        double r168001 = r168000 * r167999;
        double r168002 = cbrt(r168001);
        double r168003 = a;
        double r168004 = cbrt(r168003);
        double r168005 = r168002 / r168004;
        double r168006 = r167998 * r168005;
        return r168006;
}

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 15.8

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  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-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 cbrt-div1.2

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

  9. Applied add-cube-cbrt1.3

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

  10. Final simplification1.3

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))