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Derivation

1. Initial program 27.3

   \[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]

2. Initial simplification2.8

   \[\leadsto \frac{\cos \left(2 \cdot x\right)}{\left(sin \cdot \left(x \cdot cos\right)\right) \cdot \left(sin \cdot \left(x \cdot cos\right)\right)}\]
3. Using strategy rm

4. Applied associate-/r*2.5

   \[\leadsto \color{blue}{\frac{\frac{\cos \left(2 \cdot x\right)}{sin \cdot \left(x \cdot cos\right)}}{sin \cdot \left(x \cdot cos\right)}}\]
5. Using strategy rm

6. Applied associate-/r*2.5

   \[\leadsto \frac{\color{blue}{\frac{\frac{\cos \left(2 \cdot x\right)}{sin}}{x \cdot cos}}}{sin \cdot \left(x \cdot cos\right)}\]
7. Using strategy rm

8. Applied clear-num2.5

   \[\leadsto \frac{\color{blue}{\frac{1}{\frac{x \cdot cos}{\frac{\cos \left(2 \cdot x\right)}{sin}}}}}{sin \cdot \left(x \cdot cos\right)}\]
9. Using strategy rm

10. Applied associate-/r/2.6

    \[\leadsto \frac{\color{blue}{\frac{1}{x \cdot cos} \cdot \frac{\cos \left(2 \cdot x\right)}{sin}}}{sin \cdot \left(x \cdot cos\right)}\]

11. Applied times-frac2.6

    \[\leadsto \color{blue}{\frac{\frac{1}{x \cdot cos}}{sin} \cdot \frac{\frac{\cos \left(2 \cdot x\right)}{sin}}{x \cdot cos}}\]

12. Final simplification2.6

    \[\leadsto \frac{\frac{\cos \left(x \cdot 2\right)}{sin}}{cos \cdot x} \cdot \frac{\frac{1}{cos \cdot x}}{sin}\]

Runtime

Time bar (total: 49.3s)Debug logProfile

herbie shell --seed 2018225 +o rules:numerics
(FPCore (x cos sin)
  :name "cos(2*x)/(cos^2(x)*sin^2(x))"
  (/ (cos (* 2 x)) (* (pow cos 2) (* (* x (pow sin 2)) x))))