Average Error: 15.4 → 0.9
Time: 15.0s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}} \cdot \sqrt[3]{g}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a}} \cdot \left(\sqrt[3]{\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}} \cdot \sqrt[3]{g}\right)
double f(double g, double a) {
        double r4501509 = g;
        double r4501510 = 2.0;
        double r4501511 = a;
        double r4501512 = r4501510 * r4501511;
        double r4501513 = r4501509 / r4501512;
        double r4501514 = cbrt(r4501513);
        return r4501514;
}
↓
double f(double g, double a) {
        double r4501515 = 0.5;
        double r4501516 = cbrt(r4501515);
        double r4501517 = a;
        double r4501518 = r4501516 / r4501517;
        double r4501519 = cbrt(r4501518);
        double r4501520 = r4501516 * r4501516;
        double r4501521 = cbrt(r4501520);
        double r4501522 = g;
        double r4501523 = cbrt(r4501522);
        double r4501524 = r4501521 * r4501523;
        double r4501525 = r4501519 * r4501524;
        return r4501525;
}

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 15.4

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

  3. Applied div-inv15.4

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

  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-cube-cbrt0.8

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

  9. Applied times-frac0.8

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

  10. Applied cbrt-prod0.9

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

  11. Applied associate-*r*0.9

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

  12. Simplified0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))