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. Using strategy rm

3. Applied add-cbrt-cube1.5

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

4. Applied simplify1.0

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

6. Applied add-cube-cbrt1.0

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

7. Applied unpow-prod-down1.0

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

8. Applied cbrt-prod0.1

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

9. Applied simplify0.1

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

10. Applied simplify0.1

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

12. Applied add-cbrt-cube0.0

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

13. Applied simplify0.0

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

Runtime

Time bar (total: 31.7s)Debug logProfile

herbie shell --seed '#(1070578969 3140398606 632207097 462683394 1189254563 964980650)' 
(FPCore (g h)
  :name "2-ancestry mixing, negative discriminant"
  (* 2 (cos (+ (/ (* 2 PI) 3) (/ (acos (/ (- g) h)) 3)))))