Average Error: 0.1 → 0.4
Time: 21.9s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{\cos y} \cdot \left(x \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}}\right)\right)\right) - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{\cos y} \cdot \left(x \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}}\right)\right)\right) - z \cdot \sin y
double f(double x, double y, double z) {
        double r9303864 = x;
        double r9303865 = y;
        double r9303866 = cos(r9303865);
        double r9303867 = r9303864 * r9303866;
        double r9303868 = z;
        double r9303869 = sin(r9303865);
        double r9303870 = r9303868 * r9303869;
        double r9303871 = r9303867 - r9303870;
        return r9303871;
}
↓
double f(double x, double y, double z) {
        double r9303872 = y;
        double r9303873 = cos(r9303872);
        double r9303874 = cbrt(r9303873);
        double r9303875 = x;
        double r9303876 = cbrt(r9303874);
        double r9303877 = r9303874 * r9303874;
        double r9303878 = cbrt(r9303877);
        double r9303879 = r9303874 * r9303878;
        double r9303880 = r9303876 * r9303879;
        double r9303881 = r9303875 * r9303880;
        double r9303882 = r9303874 * r9303881;
        double r9303883 = z;
        double r9303884 = sin(r9303872);
        double r9303885 = r9303883 * r9303884;
        double r9303886 = r9303882 - r9303885;
        return r9303886;
}

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 add-cube-cbrt0.4

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

  7. Applied cbrt-prod0.4

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

  8. Applied associate-*r*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))