Average Error: 0.1 → 0.3
Time: 12.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r199780 = x;
        double r199781 = y;
        double r199782 = cos(r199781);
        double r199783 = r199780 * r199782;
        double r199784 = z;
        double r199785 = sin(r199781);
        double r199786 = r199784 * r199785;
        double r199787 = r199783 - r199786;
        return r199787;
}
↓
double f(double x, double y, double z) {
        double r199788 = x;
        double r199789 = y;
        double r199790 = cos(r199789);
        double r199791 = 2.0;
        double r199792 = pow(r199790, r199791);
        double r199793 = 0.6666666666666666;
        double r199794 = pow(r199792, r199793);
        double r199795 = 0.3333333333333333;
        double r199796 = pow(r199792, r199795);
        double r199797 = r199794 * r199796;
        double r199798 = cbrt(r199797);
        double r199799 = r199788 * r199798;
        double r199800 = cbrt(r199790);
        double r199801 = r199799 * r199800;
        double r199802 = z;
        double r199803 = sin(r199789);
        double r199804 = r199802 * r199803;
        double r199805 = r199801 - r199804;
        return r199805;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \cos y - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)} - z \cdot \sin y\]

  4. Applied associate-*r*0.4

    \[\leadsto \color{blue}{\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}} - z \cdot \sin y\]
  5. Using strategy rm

  6. Applied cbrt-unprod0.3

    \[\leadsto \left(x \cdot \color{blue}{\sqrt[3]{\cos y \cdot \cos y}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  7. Simplified0.3

    \[\leadsto \left(x \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  8. Using strategy rm

  9. Applied add-cube-cbrt0.3

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

  10. Simplified0.3

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

  12. Applied pow1/30.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))