Error

Derivation

1. Initial program 15.6

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

3. Applied div-inv15.6

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

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 cbrt-div0.9

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

7. Simplified0.9

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

8. Final simplification0.9

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

Reproduce

herbie shell --seed 2019100 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))