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Derivation

1. Initial program 15.4

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

2. Initial simplification15.4

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

4. Applied cbrt-div0.8

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

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

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

7. Applied associate-/l*0.9

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

8. Taylor expanded around 0 49.4

   \[\leadsto \frac{1}{\color{blue}{e^{\frac{1}{3} \cdot \left(\log 2 + \log a\right)} \cdot {\left(\frac{1}{g}\right)}^{\frac{1}{3}}}}\]

9. Simplified0.9

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

10. Final simplification0.9

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

Runtime

Time bar (total: 18.5s)Debug logProfile

herbie shell --seed 2018235 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))