Average Error: 16.1 → 0.9
Time: 7.7s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{2}}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{1}}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{2}}\right) \cdot \sqrt[3]{\frac{\sqrt[3]{1}}{a}}
double f(double g, double a) {
        double r121105 = g;
        double r121106 = 2.0;
        double r121107 = a;
        double r121108 = r121106 * r121107;
        double r121109 = r121105 / r121108;
        double r121110 = cbrt(r121109);
        return r121110;
}
↓
double f(double g, double a) {
        double r121111 = g;
        double r121112 = cbrt(r121111);
        double r121113 = 1.0;
        double r121114 = cbrt(r121113);
        double r121115 = r121114 * r121114;
        double r121116 = 2.0;
        double r121117 = r121115 / r121116;
        double r121118 = cbrt(r121117);
        double r121119 = r121112 * r121118;
        double r121120 = a;
        double r121121 = r121114 / r121120;
        double r121122 = cbrt(r121121);
        double r121123 = r121119 * r121122;
        return r121123;
}

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 16.1

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

  3. Applied div-inv16.1

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

  4. Applied cbrt-prod0.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.9

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

  7. Applied times-frac0.8

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

  8. Applied cbrt-prod0.9

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

  9. Applied associate-*r*0.9

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

  10. Final simplification0.9

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

Reproduce

herbie shell --seed 2019308 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))