cos(2*x)/(cos^2(x)*sin^2(x))

Average Error: 28.5 → 2.8

Time: 9.6m

Precision: 64

Math

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

↓

\[\left(\frac{\frac{\frac{1}{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}} \cdot \sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}}\right)\right) \cdot \frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x}}\]

C

double f(double x, double cos, double sin) {
        double r1348736 = 2.0;
        double r1348737 = x;
        double r1348738 = r1348736 * r1348737;
        double r1348739 = cos(r1348738);
        double r1348740 = cos;
        double r1348741 = pow(r1348740, r1348736);
        double r1348742 = sin;
        double r1348743 = pow(r1348742, r1348736);
        double r1348744 = r1348737 * r1348743;
        double r1348745 = r1348744 * r1348737;
        double r1348746 = r1348741 * r1348745;
        double r1348747 = r1348739 / r1348746;
        return r1348747;
}

↓

double f(double x, double cos, double sin) {
        double r1348748 = 1.0;
        double r1348749 = sin;
        double r1348750 = 2.0;
        double r1348751 = 2.0;
        double r1348752 = r1348750 / r1348751;
        double r1348753 = pow(r1348749, r1348752);
        double r1348754 = cbrt(r1348753);
        double r1348755 = r1348754 * r1348754;
        double r1348756 = r1348748 / r1348755;
        double r1348757 = x;
        double r1348758 = cbrt(r1348757);
        double r1348759 = r1348756 / r1348758;
        double r1348760 = cos;
        double r1348761 = pow(r1348760, r1348752);
        double r1348762 = r1348759 / r1348761;
        double r1348763 = r1348750 * r1348757;
        double r1348764 = cos(r1348763);
        double r1348765 = cbrt(r1348764);
        double r1348766 = r1348765 / r1348753;
        double r1348767 = r1348766 / r1348758;
        double r1348768 = cbrt(r1348767);
        double r1348769 = r1348768 * r1348768;
        double r1348770 = r1348758 * r1348758;
        double r1348771 = r1348769 / r1348770;
        double r1348772 = r1348754 / r1348765;
        double r1348773 = r1348765 / r1348772;
        double r1348774 = r1348773 / r1348758;
        double r1348775 = r1348774 / r1348761;
        double r1348776 = r1348771 * r1348775;
        double r1348777 = r1348762 * r1348776;
        double r1348778 = r1348768 / r1348758;
        double r1348779 = r1348777 * r1348778;
        return r1348779;
}

Error

Bits error versus x

Bits error versus cos

Bits error versus sin

Derivation

1. Initial program 28.5

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

2. Simplified 27.1

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

4. Applied add-cube-cbrt 27.3

   \[\leadsto \frac{\frac{\frac{\cos \left(2 \cdot x\right)}{{sin}^{2}}}{{cos}^{2} \cdot x}}{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}\]

5. Applied sqr-pow 27.3

   \[\leadsto \frac{\frac{\frac{\cos \left(2 \cdot x\right)}{\color{blue}{{sin}^{\left(\frac{2}{2}\right)} \cdot {sin}^{\left(\frac{2}{2}\right)}}}}{{cos}^{2} \cdot x}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]

6. Applied add-cube-cbrt 27.3

   \[\leadsto \frac{\frac{\frac{\color{blue}{\left(\sqrt[3]{\cos \left(2 \cdot x\right)} \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}\right) \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}}{{sin}^{\left(\frac{2}{2}\right)} \cdot {sin}^{\left(\frac{2}{2}\right)}}}{{cos}^{2} \cdot x}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]

7. Applied times-frac 27.1

   \[\leadsto \frac{\frac{\color{blue}{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)} \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}} \cdot \frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}}{{cos}^{2} \cdot x}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]

8. Applied times-frac 19.9

   \[\leadsto \frac{\color{blue}{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)} \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{{cos}^{2}} \cdot \frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{x}}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\]

9. Applied times-frac 19.3

   \[\leadsto \color{blue}{\frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)} \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{{cos}^{2}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{x}}{\sqrt[3]{x}}}\]

10. Simplified 17.2

    \[\leadsto \color{blue}{\frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{{sin}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{{cos}^{2}}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{x}}{\sqrt[3]{x}}\]

11. Simplified 17.2

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

13. Applied sqr-pow 17.2

    \[\leadsto \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{{sin}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{\color{blue}{{cos}^{\left(\frac{2}{2}\right)} \cdot {cos}^{\left(\frac{2}{2}\right)}}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\]

14. Applied *-un-lft-identity 17.2

    \[\leadsto \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{{sin}^{\left(\frac{2}{2}\right)}}{\color{blue}{1 \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)} \cdot {cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\]

15. Applied add-cube-cbrt 17.2

    \[\leadsto \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\color{blue}{\left(\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}\right) \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}}{1 \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)} \cdot {cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\]

16. Applied times-frac 17.2

    \[\leadsto \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\color{blue}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1} \cdot \frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)} \cdot {cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\]

17. Applied *-un-lft-identity 17.2

    \[\leadsto \frac{\frac{\frac{\color{blue}{1 \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1} \cdot \frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)} \cdot {cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\]

18. Applied times-frac 17.2

    \[\leadsto \frac{\frac{\color{blue}{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}} \cdot \frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)} \cdot {cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\]

19. Applied times-frac 17.2

    \[\leadsto \frac{\color{blue}{\frac{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}}}{\sqrt[3]{x}} \cdot \frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}}{{cos}^{\left(\frac{2}{2}\right)} \cdot {cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\]

20. Applied times-frac 10.4

    \[\leadsto \color{blue}{\left(\frac{\frac{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}}\right)} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\]

21. Applied associate-*l* 5.3

    \[\leadsto \color{blue}{\frac{\frac{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{x}\right)}\]
22. Using strategy rm

23. Applied add-cube-cbrt 5.4

    \[\leadsto \frac{\frac{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}}\right)\]

24. Applied add-cube-cbrt 5.5

    \[\leadsto \frac{\frac{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\color{blue}{\left(\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}} \cdot \sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}\right) \cdot \sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}}\right)\]

25. Applied times-frac 5.5

    \[\leadsto \frac{\frac{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \color{blue}{\left(\frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}} \cdot \sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x}}\right)}\right)\]

26. Applied associate-*r* 2.1

    \[\leadsto \frac{\frac{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \color{blue}{\left(\left(\frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}} \cdot \sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right) \cdot \frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x}}\right)}\]
27. Using strategy rm

28. Applied associate-*r* 2.8

    \[\leadsto \color{blue}{\left(\frac{\frac{\frac{1}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{1}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}} \cdot \sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right)\right) \cdot \frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x}}}\]

29. Final simplification 2.8

    \[\leadsto \left(\frac{\frac{\frac{1}{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}} \cdot \sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\frac{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}}\right)\right) \cdot \frac{\sqrt[3]{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}}}}{\sqrt[3]{x}}\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x cos sin)
  :name "cos(2*x)/(cos^2(x)*sin^2(x))"
  (/ (cos (* 2.0 x)) (* (pow cos 2.0) (* (* x (pow sin 2.0)) x))))