Error

Derivation

1. Initial program 15.1

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

3. Applied add-sqr-sqrt15.2

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

4. Applied associate-*l*15.2

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

5. Applied associate-/r*15.2

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

6. Applied cbrt-div0.8

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

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

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

9. Applied associate-/l*0.9

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

10. Applied cbrt-div0.9

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

11. Simplified0.9

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

12. Final simplification0.9

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

Reproduce

herbie shell --seed 2019088 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))