Average Error: 15.6 → 0.9
Time: 15.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\sqrt{\frac{1}{2}}} \cdot \sqrt[3]{\sqrt{\frac{1}{2}} \cdot \frac{1}{a}}\right) \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\sqrt{\frac{1}{2}}} \cdot \sqrt[3]{\sqrt{\frac{1}{2}} \cdot \frac{1}{a}}\right) \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r5688514 = g;
        double r5688515 = 2.0;
        double r5688516 = a;
        double r5688517 = r5688515 * r5688516;
        double r5688518 = r5688514 / r5688517;
        double r5688519 = cbrt(r5688518);
        return r5688519;
}
↓
double f(double g, double a) {
        double r5688520 = 0.5;
        double r5688521 = sqrt(r5688520);
        double r5688522 = cbrt(r5688521);
        double r5688523 = 1.0;
        double r5688524 = a;
        double r5688525 = r5688523 / r5688524;
        double r5688526 = r5688521 * r5688525;
        double r5688527 = cbrt(r5688526);
        double r5688528 = r5688522 * r5688527;
        double r5688529 = g;
        double r5688530 = cbrt(r5688529);
        double r5688531 = r5688528 * r5688530;
        return r5688531;
}

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 div-inv15.6

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

  4. Applied cbrt-prod0.9

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

  5. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{\frac{1}{2}}{a}}}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.8

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

  8. Applied add-sqr-sqrt0.8

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

  9. Applied times-frac0.8

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

  10. Applied cbrt-prod0.9

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

  11. Simplified0.9

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

  13. Applied div-inv0.9

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

  14. Final simplification0.9

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))