Average Error: 15.7 → 1.2
Time: 6.5s
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 r131503 = g;
        double r131504 = 2.0;
        double r131505 = a;
        double r131506 = r131504 * r131505;
        double r131507 = r131503 / r131506;
        double r131508 = cbrt(r131507);
        return r131508;
}
↓
double f(double g, double a) {
        double r131509 = g;
        double r131510 = cbrt(r131509);
        double r131511 = r131510 * r131510;
        double r131512 = 2.0;
        double r131513 = r131511 / r131512;
        double r131514 = cbrt(r131513);
        double r131515 = sqrt(r131514);
        double r131516 = r131515 * r131515;
        double r131517 = cbrt(r131510);
        double r131518 = a;
        double r131519 = cbrt(r131518);
        double r131520 = r131517 / r131519;
        double r131521 = r131516 * r131520;
        return r131521;
}

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 15.7

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

  3. Applied add-cube-cbrt15.9

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

  4. Applied times-frac15.9

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

  5. Applied cbrt-prod5.9

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

  7. Applied cbrt-div1.1

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \color{blue}{\frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}}\]
  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 2020062 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))