Average Error: 15.5 → 0.8
Time: 11.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{1}{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{1}{a}}
double f(double g, double a) {
        double r138103 = g;
        double r138104 = 2.0;
        double r138105 = a;
        double r138106 = r138104 * r138105;
        double r138107 = r138103 / r138106;
        double r138108 = cbrt(r138107);
        return r138108;
}
↓
double f(double g, double a) {
        double r138109 = 1.0;
        double r138110 = 2.0;
        double r138111 = r138109 / r138110;
        double r138112 = cbrt(r138111);
        double r138113 = g;
        double r138114 = cbrt(r138113);
        double r138115 = r138112 * r138114;
        double r138116 = a;
        double r138117 = r138109 / r138116;
        double r138118 = cbrt(r138117);
        double r138119 = r138115 * r138118;
        return r138119;
}

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 15.5

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

  3. Applied div-inv15.5

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

  4. Applied cbrt-prod0.8

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

  6. Applied *-un-lft-identity0.8

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

  7. Applied times-frac0.8

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

  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. Simplified0.8

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

  11. Final simplification0.8

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))