Average Error: 15.4 → 0.9
Time: 15.9s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot g\right) \cdot \sqrt[3]{\frac{1}{2}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot g\right) \cdot \sqrt[3]{\frac{1}{2}}}
double f(double g, double a) {
        double r4498374 = g;
        double r4498375 = 2.0;
        double r4498376 = a;
        double r4498377 = r4498375 * r4498376;
        double r4498378 = r4498374 / r4498377;
        double r4498379 = cbrt(r4498378);
        return r4498379;
}
↓
double f(double g, double a) {
        double r4498380 = 1.0;
        double r4498381 = a;
        double r4498382 = r4498380 / r4498381;
        double r4498383 = cbrt(r4498382);
        double r4498384 = 0.5;
        double r4498385 = cbrt(r4498384);
        double r4498386 = r4498385 * r4498385;
        double r4498387 = g;
        double r4498388 = r4498386 * r4498387;
        double r4498389 = r4498388 * r4498385;
        double r4498390 = cbrt(r4498389);
        double r4498391 = r4498383 * r4498390;
        return r4498391;
}

Error

Bits error versus g

Bits error versus a

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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 div-inv0.8

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

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

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

  11. Applied add-cbrt-cube1.0

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

  12. Simplified0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2019130 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))