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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-div0.8

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

6. Applied clear-num0.8

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

7. Taylor expanded around inf 48.4

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

8. Simplified0.9

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

9. Final simplification0.9

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

Runtime

Time bar (total: 16.6s)Debug logProfile

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