Average Error: 27.3 → 2.7

Time: 24.4s

Precision: 64

Internal Precision: 128

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

↓

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

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Initial program 27.3
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
Initial simplification2.9
\[\leadsto \frac{\cos \left(2 \cdot x\right)}{\left(\left(x \cdot cos\right) \cdot sin\right) \cdot \left(\left(x \cdot cos\right) \cdot sin\right)}\]
Using strategy rm
Applied div-inv2.9
\[\leadsto \color{blue}{\cos \left(2 \cdot x\right) \cdot \frac{1}{\left(\left(x \cdot cos\right) \cdot sin\right) \cdot \left(\left(x \cdot cos\right) \cdot sin\right)}}\]
Using strategy rm
Applied associate-/r*2.7
\[\leadsto \cos \left(2 \cdot x\right) \cdot \color{blue}{\frac{\frac{1}{\left(x \cdot cos\right) \cdot sin}}{\left(x \cdot cos\right) \cdot sin}}\]
Final simplification2.7
\[\leadsto \frac{\frac{1}{sin \cdot \left(cos \cdot x\right)}}{sin \cdot \left(cos \cdot x\right)} \cdot \cos \left(2 \cdot x\right)\]

	Baseline	Herbie	Oracle	Span	%
Regimes	2.7	2.7	1.7	1.0	0%

herbie shell --seed 2018351 
(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))))