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Derivation

1. Initial program 15.6

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

2. Initial simplification15.6

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

4. Applied cbrt-div0.9

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

6. Applied div-inv0.9

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

7. Taylor expanded around 0 33.9

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

8. Simplified0.9

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

9. Final simplification0.9

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

Runtime

Time bar (total: 11.9s)Debug logProfile

herbie shell --seed 2018340 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))