Average Error: 15.9 → 1.1
Time: 6.0s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \frac{\sqrt[3]{{\left(\sqrt[3]{g}\right)}^{1}}}{\sqrt[3]{a}}\]
\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]{g}\right)}^{1}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r198452 = g;
        double r198453 = 2.0;
        double r198454 = a;
        double r198455 = r198453 * r198454;
        double r198456 = r198452 / r198455;
        double r198457 = cbrt(r198456);
        return r198457;
}
↓
double f(double g, double a) {
        double r198458 = g;
        double r198459 = cbrt(r198458);
        double r198460 = r198459 * r198459;
        double r198461 = 2.0;
        double r198462 = r198460 / r198461;
        double r198463 = cbrt(r198462);
        double r198464 = 1.0;
        double r198465 = pow(r198459, r198464);
        double r198466 = cbrt(r198465);
        double r198467 = a;
        double r198468 = cbrt(r198467);
        double r198469 = r198466 / r198468;
        double r198470 = r198463 * r198469;
        return r198470;
}

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-cbrt16.1

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

  4. Applied times-frac16.1

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

  5. Applied cbrt-prod5.7

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

  7. Applied cbrt-div1.1

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

  9. Applied pow11.1

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

  10. Final simplification1.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))