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Derivation

1. Initial program 15.6

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

3. Applied cbrt-div0.8

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

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

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

6. Applied associate-/l*0.8

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

7. Taylor expanded around 0 48.4

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

8. Simplified0.9

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

10. Applied associate-/r*0.9

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

11. Final simplification0.9

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

Runtime

Time bar (total: 17.3s)Debug logProfile

herbie shell --seed 2018248 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))