Average Error: 15.6 → 0.8
Time: 10.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}\right)} \cdot \sqrt[3]{g}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{\sqrt[3]{\frac{1}{2}}}{a} \cdot \left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}\right)} \cdot \sqrt[3]{g}
double f(double g, double a) {
        double r2855058 = g;
        double r2855059 = 2.0;
        double r2855060 = a;
        double r2855061 = r2855059 * r2855060;
        double r2855062 = r2855058 / r2855061;
        double r2855063 = cbrt(r2855062);
        return r2855063;
}
↓
double f(double g, double a) {
        double r2855064 = 0.5;
        double r2855065 = cbrt(r2855064);
        double r2855066 = a;
        double r2855067 = r2855065 / r2855066;
        double r2855068 = r2855065 * r2855065;
        double r2855069 = r2855067 * r2855068;
        double r2855070 = cbrt(r2855069);
        double r2855071 = g;
        double r2855072 = cbrt(r2855071);
        double r2855073 = r2855070 * r2855072;
        return r2855073;
}

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. Taylor expanded around 0 34.5

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

  7. Simplified0.8

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

  9. Applied add-cbrt-cube1.0

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

  10. Simplified0.9

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

  12. Applied associate-*r*0.9

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

  13. Simplified0.8

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

  14. Final simplification0.8

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

Reproduce

herbie shell --seed 2019154 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))