Average Error: 27.7 → 2.7
Time: 38.2s
Precision: 64
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
↓
\[\frac{\sqrt[3]{\cos \left(2 \cdot x\right)} \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}{\left(sin \cdot x\right) \cdot cos} \cdot \frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\left(sin \cdot x\right) \cdot cos}\]
\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}
↓
\frac{\sqrt[3]{\cos \left(2 \cdot x\right)} \cdot \sqrt[3]{\cos \left(2 \cdot x\right)}}{\left(sin \cdot x\right) \cdot cos} \cdot \frac{\sqrt[3]{\cos \left(2 \cdot x\right)}}{\left(sin \cdot x\right) \cdot cos}
double f(double x, double cos, double sin) {
        double r3453868 = 2.0;
        double r3453869 = x;
        double r3453870 = r3453868 * r3453869;
        double r3453871 = cos(r3453870);
        double r3453872 = cos;
        double r3453873 = pow(r3453872, r3453868);
        double r3453874 = sin;
        double r3453875 = pow(r3453874, r3453868);
        double r3453876 = r3453869 * r3453875;
        double r3453877 = r3453876 * r3453869;
        double r3453878 = r3453873 * r3453877;
        double r3453879 = r3453871 / r3453878;
        return r3453879;
}
↓
double f(double x, double cos, double sin) {
        double r3453880 = 2.0;
        double r3453881 = x;
        double r3453882 = r3453880 * r3453881;
        double r3453883 = cos(r3453882);
        double r3453884 = cbrt(r3453883);
        double r3453885 = r3453884 * r3453884;
        double r3453886 = sin;
        double r3453887 = r3453886 * r3453881;
        double r3453888 = cos;
        double r3453889 = r3453887 * r3453888;
        double r3453890 = r3453885 / r3453889;
        double r3453891 = r3453884 / r3453889;
        double r3453892 = r3453890 * r3453891;
        return r3453892;
}

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 27.7

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

  2. Simplified2.8

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

  4. Applied add-cube-cbrt2.9

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

  5. Applied times-frac2.7

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

  6. Final simplification2.7

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

Reproduce

herbie shell --seed 2019144 
(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))))