Average Error: 27.8 → 2.9
Time: 1.7m
Precision: 64
\[\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}\]
↓
\[\frac{\frac{\cos \left(2 \cdot x\right)}{\left(cos \cdot x\right) \cdot sin}}{\left(\sqrt[3]{sin} \cdot \sqrt[3]{sin}\right) \cdot \left(\sqrt[3]{sin} \cdot \left(cos \cdot x\right)\right)}\]
\frac{\cos \left(2 \cdot x\right)}{{cos}^{2} \cdot \left(\left(x \cdot {sin}^{2}\right) \cdot x\right)}
↓
\frac{\frac{\cos \left(2 \cdot x\right)}{\left(cos \cdot x\right) \cdot sin}}{\left(\sqrt[3]{sin} \cdot \sqrt[3]{sin}\right) \cdot \left(\sqrt[3]{sin} \cdot \left(cos \cdot x\right)\right)}
double f(double x, double cos, double sin) {
        double r12297769 = 2.0;
        double r12297770 = x;
        double r12297771 = r12297769 * r12297770;
        double r12297772 = cos(r12297771);
        double r12297773 = cos;
        double r12297774 = pow(r12297773, r12297769);
        double r12297775 = sin;
        double r12297776 = pow(r12297775, r12297769);
        double r12297777 = r12297770 * r12297776;
        double r12297778 = r12297777 * r12297770;
        double r12297779 = r12297774 * r12297778;
        double r12297780 = r12297772 / r12297779;
        return r12297780;
}
↓
double f(double x, double cos, double sin) {
        double r12297781 = 2.0;
        double r12297782 = x;
        double r12297783 = r12297781 * r12297782;
        double r12297784 = cos(r12297783);
        double r12297785 = cos;
        double r12297786 = r12297785 * r12297782;
        double r12297787 = sin;
        double r12297788 = r12297786 * r12297787;
        double r12297789 = r12297784 / r12297788;
        double r12297790 = cbrt(r12297787);
        double r12297791 = r12297790 * r12297790;
        double r12297792 = r12297790 * r12297786;
        double r12297793 = r12297791 * r12297792;
        double r12297794 = r12297789 / r12297793;
        return r12297794;
}

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. Simplified2.8

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

  4. Applied associate-/r*2.5

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

  6. Applied add-cube-cbrt2.9

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

  7. Applied associate-*l*2.9

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

  8. Final simplification2.9

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

Reproduce

herbie shell --seed 2019119 
(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))))