Average Error: 15.8 → 0.9
Time: 13.2s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\sqrt[3]{\frac{1}{g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\sqrt[3]{\frac{1}{g}}}
double f(double g, double a) {
        double r120877 = g;
        double r120878 = 2.0;
        double r120879 = a;
        double r120880 = r120878 * r120879;
        double r120881 = r120877 / r120880;
        double r120882 = cbrt(r120881);
        return r120882;
}
↓
double f(double g, double a) {
        double r120883 = 1.0;
        double r120884 = 2.0;
        double r120885 = a;
        double r120886 = r120884 * r120885;
        double r120887 = cbrt(r120886);
        double r120888 = r120883 / r120887;
        double r120889 = g;
        double r120890 = r120883 / r120889;
        double r120891 = cbrt(r120890);
        double r120892 = r120888 / r120891;
        return r120892;
}

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 15.8

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

  3. Applied cbrt-div0.8

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

  5. Applied clear-num0.8

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

  7. Applied div-inv0.9

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

  8. Applied associate-/r*0.9

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

  10. Applied add-cbrt-cube0.9

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

  11. Applied cbrt-undiv0.9

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

  12. Simplified0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))