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Derivation

1. Initial program 27.9

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

2. Initial simplification2.9

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

4. Applied cos-23.0

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

5. Applied div-sub3.0

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

6. Final simplification3.0

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

Runtime

Time bar (total: 16.9s)Debug logProfile

herbie shell --seed 2018290 
(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))))