Average Error: 28.0 → 1.9
Time: 2.0m
Precision: 64
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
↓
\[\left(\frac{\frac{\frac{\cos \left(2 \cdot x\right)}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}} \cdot \frac{\frac{\sqrt[3]{\sqrt[3]{\frac{1}{{sin}^{\left(\frac{2}{2}\right)}}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}}}{x} \cdot \frac{\frac{1}{\sqrt[3]{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}}}{{1}^{\left(\frac{2}{2}\right)}}\right) \cdot \frac{\frac{\sqrt[3]{\frac{1}{{sin}^{\left(\frac{2}{2}\right)}}} \cdot \sqrt[3]{\frac{1}{{sin}^{\left(\frac{2}{2}\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}}\]
\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}
↓
\left(\frac{\frac{\frac{\cos \left(2 \cdot x\right)}{{sin}^{\left(\frac{2}{2}\right)}}}{\sqrt[3]{x}} \cdot \frac{\frac{\sqrt[3]{\sqrt[3]{\frac{1}{{sin}^{\left(\frac{2}{2}\right)}}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}}}{x} \cdot \frac{\frac{1}{\sqrt[3]{\sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}} \cdot \sqrt[3]{{sin}^{\left(\frac{2}{2}\right)}}}}}{{1}^{\left(\frac{2}{2}\right)}}\right) \cdot \frac{\frac{\sqrt[3]{\frac{1}{{sin}^{\left(\frac{2}{2}\right)}}} \cdot \sqrt[3]{\frac{1}{{sin}^{\left(\frac{2}{2}\right)}}}}{\sqrt[3]{x}}}{{cos}^{\left(\frac{2}{2}\right)}}
double f(double x, double cos, double sin) {
        double r249567 = 2.0;
        double r249568 = x;
        double r249569 = r249567 * r249568;
        double r249570 = cos(r249569);
        double r249571 = cos;
        double r249572 = pow(r249571, r249567);
        double r249573 = sin;
        double r249574 = pow(r249573, r249567);
        double r249575 = r249568 * r249574;
        double r249576 = r249575 * r249568;
        double r249577 = r249572 * r249576;
        double r249578 = r249570 / r249577;
        return r249578;
}
↓
double f(double x, double cos, double sin) {
        double r249579 = 2.0;
        double r249580 = x;
        double r249581 = r249579 * r249580;
        double r249582 = cos(r249581);
        double r249583 = sin;
        double r249584 = 2.0;
        double r249585 = r249579 / r249584;
        double r249586 = pow(r249583, r249585);
        double r249587 = r249582 / r249586;
        double r249588 = cbrt(r249580);
        double r249589 = r249587 / r249588;
        double r249590 = 1.0;
        double r249591 = r249590 / r249586;
        double r249592 = cbrt(r249591);
        double r249593 = cbrt(r249592);
        double r249594 = r249593 / r249588;
        double r249595 = cos;
        double r249596 = pow(r249595, r249585);
        double r249597 = r249594 / r249596;
        double r249598 = r249589 * r249597;
        double r249599 = r249598 / r249580;
        double r249600 = cbrt(r249586);
        double r249601 = r249600 * r249600;
        double r249602 = cbrt(r249601);
        double r249603 = r249590 / r249602;
        double r249604 = pow(r249590, r249585);
        double r249605 = r249603 / r249604;
        double r249606 = r249599 * r249605;
        double r249607 = r249592 * r249592;
        double r249608 = r249607 / r249588;
        double r249609 = r249608 / r249596;
        double r249610 = r249606 * r249609;
        return r249610;
}

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 28.0

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

  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 *-un-lft-identity26.8

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

  7. Applied times-frac26.6

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

  8. Applied times-frac19.9

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

  9. Applied times-frac19.2

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

  10. Simplified16.9

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

  11. Simplified20.0

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

  13. Applied sqr-pow20.0

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

  14. Applied add-cube-cbrt20.0

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

  15. Applied times-frac20.0

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

  16. Applied times-frac13.7

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

  17. Applied associate-*l*9.8

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

  18. Simplified5.3

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

  20. Applied *-un-lft-identity5.3

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

  21. Applied unpow-prod-down5.3

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

  22. Applied *-un-lft-identity5.3

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

  23. Applied add-cube-cbrt5.3

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

  24. Applied cbrt-prod5.3

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

  25. Applied times-frac5.3

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

  26. Applied times-frac5.3

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

  27. Applied associate-*l*5.4

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

  28. Simplified2.0

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

  30. Applied cbrt-div1.9

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

  31. Applied cbrt-div1.9

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

  32. Applied frac-times1.9

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

  33. Applied cbrt-div1.9

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

  34. Final simplification1.9

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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))))