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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `x`

Derivation

Initial program 27.4
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
Simplified2.8
\[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{\left(sin \cdot \left(x \cdot cos\right)\right) \cdot \left(sin \cdot \left(x \cdot cos\right)\right)}}\]
Taylor expanded around -inf 30.8
\[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{{sin}^{2} \cdot \left({x}^{2} \cdot {cos}^{2}\right)}}\]
Simplified2.7
\[\leadsto \color{blue}{\frac{\cos \left(2 \cdot x\right)}{\left(\left(x \cdot sin\right) \cdot cos\right) \cdot \left(\left(x \cdot sin\right) \cdot cos\right)}}\]
Final simplification2.7
\[\leadsto \frac{\cos \left(2 \cdot x\right)}{\left(\left(x \cdot sin\right) \cdot cos\right) \cdot \left(\left(x \cdot sin\right) \cdot cos\right)}\]

Reproduce

herbie shell --seed 2019072 +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))))