Average Error: 15.6 → 1.3
Time: 5.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\sqrt[3]{a} \cdot \sqrt[3]{a}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{a}}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \left(\sqrt[3]{\frac{1}{\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 r152081 = g;
        double r152082 = 2.0;
        double r152083 = a;
        double r152084 = r152082 * r152083;
        double r152085 = r152081 / r152084;
        double r152086 = cbrt(r152085);
        return r152086;
}
↓
double f(double g, double a) {
        double r152087 = g;
        double r152088 = cbrt(r152087);
        double r152089 = r152088 * r152088;
        double r152090 = 2.0;
        double r152091 = r152089 / r152090;
        double r152092 = cbrt(r152091);
        double r152093 = 1.0;
        double r152094 = a;
        double r152095 = cbrt(r152094);
        double r152096 = r152095 * r152095;
        double r152097 = r152093 / r152096;
        double r152098 = cbrt(r152097);
        double r152099 = r152088 / r152095;
        double r152100 = cbrt(r152099);
        double r152101 = r152098 * r152100;
        double r152102 = r152092 * r152101;
        return r152102;
}

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-prod5.9

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

  7. Applied add-cube-cbrt6.0

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

  8. Applied *-un-lft-identity6.0

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

  9. Applied cbrt-prod6.0

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

  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. Final simplification1.3

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

Reproduce

herbie shell --seed 2019356 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))