Average Error: 15.4 → 1.2
Time: 11.3s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}} \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}} \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r546 = g;
        double r547 = 2.0;
        double r548 = a;
        double r549 = r547 * r548;
        double r550 = r546 / r549;
        double r551 = cbrt(r550);
        return r551;
}
↓
double f(double g, double a) {
        double r552 = g;
        double r553 = cbrt(r552);
        double r554 = r553 * r553;
        double r555 = 2.0;
        double r556 = r554 / r555;
        double r557 = cbrt(r556);
        double r558 = sqrt(r557);
        double r559 = r558 * r558;
        double r560 = cbrt(r553);
        double r561 = a;
        double r562 = cbrt(r561);
        double r563 = r560 / r562;
        double r564 = r559 * r563;
        return r564;
}

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 add-cube-cbrt15.6

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

  4. Applied times-frac15.6

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

  5. Applied cbrt-prod5.6

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

  7. Applied cbrt-div1.2

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

  9. Applied add-sqr-sqrt1.2

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

  10. Final simplification1.2

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

Reproduce

herbie shell --seed 2020025 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))