Average Error: 28.0 → 3.0
Time: 30.8s
Precision: 64
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
↓
\[\frac{\sqrt[3]{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot sin\right) \cdot cos}} \cdot \sqrt[3]{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot sin\right) \cdot cos}}}{\frac{\left(x \cdot sin\right) \cdot cos}{\sqrt[3]{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot sin\right) \cdot cos}}}}\]
\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}
↓
\frac{\sqrt[3]{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot sin\right) \cdot cos}} \cdot \sqrt[3]{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot sin\right) \cdot cos}}}{\frac{\left(x \cdot sin\right) \cdot cos}{\sqrt[3]{\frac{\cos \left(2 \cdot x\right)}{\left(x \cdot sin\right) \cdot cos}}}}
double f(double x, double cos, double sin) {
        double r2125428 = 2.0;
        double r2125429 = x;
        double r2125430 = r2125428 * r2125429;
        double r2125431 = cos(r2125430);
        double r2125432 = cos;
        double r2125433 = pow(r2125432, r2125428);
        double r2125434 = sin;
        double r2125435 = pow(r2125434, r2125428);
        double r2125436 = r2125429 * r2125435;
        double r2125437 = r2125436 * r2125429;
        double r2125438 = r2125433 * r2125437;
        double r2125439 = r2125431 / r2125438;
        return r2125439;
}
↓
double f(double x, double cos, double sin) {
        double r2125440 = 2.0;
        double r2125441 = x;
        double r2125442 = r2125440 * r2125441;
        double r2125443 = cos(r2125442);
        double r2125444 = sin;
        double r2125445 = r2125441 * r2125444;
        double r2125446 = cos;
        double r2125447 = r2125445 * r2125446;
        double r2125448 = r2125443 / r2125447;
        double r2125449 = cbrt(r2125448);
        double r2125450 = r2125449 * r2125449;
        double r2125451 = r2125447 / r2125449;
        double r2125452 = r2125450 / r2125451;
        return r2125452;
}

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. Simplified2.9

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

  4. Applied associate-/r*2.6

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

  6. Applied add-cube-cbrt3.0

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

  7. Applied associate-/l*3.0

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

  8. Final simplification3.0

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

Reproduce

herbie shell --seed 2019151 
(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))))