Average Error: 27.8 → 2.0
Time: 7.5m
Precision: 64
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
↓
\[\frac{\frac{\frac{1}{\sqrt[3]{\frac{{sin}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}} \cdot \sqrt[3]{\frac{{sin}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\left(\frac{\sqrt[3]{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\sqrt[3]{\frac{{sin}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}}\right) \cdot \frac{\frac{\sqrt[3]{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}}{\sqrt[3]{x}}}{\sqrt[3]{x}}\right)\]
\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}
↓
\frac{\frac{\frac{1}{\sqrt[3]{\frac{{sin}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}} \cdot \sqrt[3]{\frac{{sin}^{\left(\frac{2}{2}\right)}}{\sqrt[3]{\cos \left(2 \cdot x\right)}}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}} \cdot \left(\left(\frac{\sqrt[3]{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}} \cdot \sqrt[3]{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}}{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \frac{\frac{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\sqrt[3]{\frac{{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{\sqrt[3]{\frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{{sin}^{\left(\frac{2}{2}\right)}}}}{\sqrt[3]{x}}}{\sqrt[3]{x}}\right)
double f(double x, double cos, double sin) {
        double r960093 = 2.0;
        double r960094 = x;
        double r960095 = r960093 * r960094;
        double r960096 = cos(r960095);
        double r960097 = cos;
        double r960098 = pow(r960097, r960093);
        double r960099 = sin;
        double r960100 = pow(r960099, r960093);
        double r960101 = r960094 * r960100;
        double r960102 = r960101 * r960094;
        double r960103 = r960098 * r960102;
        double r960104 = r960096 / r960103;
        return r960104;
}
↓
double f(double x, double cos, double sin) {
        double r960105 = 1.0;
        double r960106 = sin;
        double r960107 = 2.0;
        double r960108 = 2.0;
        double r960109 = r960107 / r960108;
        double r960110 = pow(r960106, r960109);
        double r960111 = x;
        double r960112 = r960107 * r960111;
        double r960113 = cos(r960112);
        double r960114 = cbrt(r960113);
        double r960115 = r960110 / r960114;
        double r960116 = cbrt(r960115);
        double r960117 = r960116 * r960116;
        double r960118 = r960105 / r960117;
        double r960119 = cbrt(r960111);
        double r960120 = r960118 / r960119;
        double r960121 = cos;
        double r960122 = pow(r960121, r960109);
        double r960123 = r960120 / r960122;
        double r960124 = r960114 / r960110;
        double r960125 = cbrt(r960124);
        double r960126 = r960125 * r960125;
        double r960127 = r960119 * r960119;
        double r960128 = r960126 / r960127;
        double r960129 = r960114 / r960116;
        double r960130 = r960129 / r960119;
        double r960131 = r960130 / r960122;
        double r960132 = r960128 * r960131;
        double r960133 = r960125 / r960119;
        double r960134 = r960133 / r960119;
        double r960135 = r960132 * r960134;
        double r960136 = r960123 * r960135;
        return r960136;
}

Error

Bits error versus x

Bits error versus cos

Bits error versus sin

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 27.8

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

  2. Simplified26.6

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

  4. Applied add-cube-cbrt26.8

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

  5. Applied sqr-pow26.8

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

  6. Applied add-cube-cbrt26.8

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

  7. Applied times-frac26.6

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

  8. Applied times-frac20.0

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

  9. Applied times-frac19.6

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

  10. Simplified17.1

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

  11. Simplified17.1

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

  13. Applied sqr-pow17.1

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

  14. Applied add-cube-cbrt17.2

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

  15. Applied *-un-lft-identity17.2

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

  16. Applied cbrt-prod17.2

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

  17. Applied times-frac17.2

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

  18. Applied times-frac17.2

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

  19. Applied times-frac10.3

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

  20. Applied associate-*l*5.2

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

  22. Applied add-cube-cbrt5.4

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

  23. Applied *-un-lft-identity5.4

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

  24. Applied cbrt-prod5.4

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

  25. Applied add-cube-cbrt5.4

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

  26. Applied times-frac5.4

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

  27. Applied times-frac5.4

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

  28. Applied associate-*r*2.0

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

  29. Final simplification2.0

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

Reproduce

herbie shell --seed 2019196 
(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))))