Error

Derivation

1. Initial program 1.0

   \[2 \cdot \cos \left(\frac{2 \cdot \pi}{3} + \frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right)\]

2. Initial simplification1.0

   \[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}\right))_*\right) \cdot 2\]
3. Using strategy rm

4. Applied add-cube-cbrt1.0

   \[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \color{blue}{\left(\left(\sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}} \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right)})_*\right) \cdot 2\]
5. Using strategy rm

6. Applied cbrt-div1.0

   \[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\left(\color{blue}{\frac{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)}}{\sqrt[3]{3}}} \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right) \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right) \cdot 2\]

7. Applied associate-*l/1.0

   \[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\color{blue}{\frac{\sqrt[3]{\cos^{-1} \left(\frac{-g}{h}\right)} \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}}{\sqrt[3]{3}}} \cdot \sqrt[3]{\frac{\cos^{-1} \left(\frac{-g}{h}\right)}{3}}\right))_*\right) \cdot 2\]

8. Final simplification1.0

   \[\leadsto \cos \left((\frac{2}{3} \cdot \pi + \left(\sqrt[3]{\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}} \cdot \frac{\sqrt[3]{\cos^{-1} \left(-\frac{g}{h}\right)} \cdot \sqrt[3]{\frac{\cos^{-1} \left(-\frac{g}{h}\right)}{3}}}{\sqrt[3]{3}}\right))_*\right) \cdot 2\]

Runtime

Time bar (total: 16.7s)Debug logProfile

herbie shell --seed 2018248 +o rules:numerics
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))