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Derivation

1. Initial program 15.7

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

2. Initial simplification15.7

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

4. Applied div-inv15.7

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

5. Applied cbrt-prod0.8

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

6. Taylor expanded around -inf 0.8

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

8. Applied cbrt-div0.9

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

10. Applied associate-*r/0.9

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

11. Final simplification0.9

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

Reproduce

herbie shell --seed 2018365 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))

Details

Time bar (total: 8.1s)Debug log