Error

Try it out

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 div-inv15.4

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

5. Applied cbrt-prod0.8

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

7. Applied cbrt-div0.8

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

8. Simplified0.8

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

9. Final simplification0.8

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

Runtime

Time bar (total: 11.1s)Debug logProfile

herbie shell --seed 2018274 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))