Error

Derivation

1. Initial program 14.8

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

3. Applied cbrt-div0.8

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

4. Taylor expanded around -inf 62.8

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

5. Applied simplify0.8

   \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{-1}{2}} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{\frac{-1}{a}}}\]
6. Using strategy rm

7. Applied cbrt-div0.9

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

8. Taylor expanded around 0 33.9

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

9. Applied simplify0.9

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

Runtime

Time bar (total: 20.4s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))