Average Error: 27.4 → 2.6
Time: 35.3s
Precision: 64
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
↓
\[\frac{\frac{\frac{\frac{\cos \left(2 \cdot x\right)}{sin}}{x}}{cos}}{\left(x \cdot sin\right) \cdot cos}\]
\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}
↓
\frac{\frac{\frac{\frac{\cos \left(2 \cdot x\right)}{sin}}{x}}{cos}}{\left(x \cdot sin\right) \cdot cos}
double f(double x, double cos, double sin) {
        double r2216648 = 2.0;
        double r2216649 = x;
        double r2216650 = r2216648 * r2216649;
        double r2216651 = cos(r2216650);
        double r2216652 = cos;
        double r2216653 = pow(r2216652, r2216648);
        double r2216654 = sin;
        double r2216655 = pow(r2216654, r2216648);
        double r2216656 = r2216649 * r2216655;
        double r2216657 = r2216656 * r2216649;
        double r2216658 = r2216653 * r2216657;
        double r2216659 = r2216651 / r2216658;
        return r2216659;
}
↓
double f(double x, double cos, double sin) {
        double r2216660 = 2.0;
        double r2216661 = x;
        double r2216662 = r2216660 * r2216661;
        double r2216663 = cos(r2216662);
        double r2216664 = sin;
        double r2216665 = r2216663 / r2216664;
        double r2216666 = r2216665 / r2216661;
        double r2216667 = cos;
        double r2216668 = r2216666 / r2216667;
        double r2216669 = r2216661 * r2216664;
        double r2216670 = r2216669 * r2216667;
        double r2216671 = r2216668 / r2216670;
        return r2216671;
}

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 27.4

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

  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 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 associate-/r*2.7

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

  8. Applied *-un-lft-identity2.7

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

  9. Applied associate-/r*2.7

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

  10. Simplified2.6

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

  11. Final simplification2.6

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

Reproduce

herbie shell --seed 2019138 
(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))))