Average Error: 0.1 → 0.4
Time: 5.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \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
double f(double x, double y, double z) {
        double r231961 = x;
        double r231962 = y;
        double r231963 = cos(r231962);
        double r231964 = r231961 * r231963;
        double r231965 = z;
        double r231966 = sin(r231962);
        double r231967 = r231965 * r231966;
        double r231968 = r231964 - r231967;
        return r231968;
}
↓
double f(double x, double y, double z) {
        double r231969 = x;
        double r231970 = y;
        double r231971 = cos(r231970);
        double r231972 = cbrt(r231971);
        double r231973 = r231972 * r231972;
        double r231974 = cbrt(r231973);
        double r231975 = r231972 * r231974;
        double r231976 = cbrt(r231972);
        double r231977 = r231975 * r231976;
        double r231978 = r231969 * r231977;
        double r231979 = r231978 * r231972;
        double r231980 = z;
        double r231981 = sin(r231970);
        double r231982 = r231980 * r231981;
        double r231983 = r231979 - r231982;
        return r231983;
}

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

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

Reproduce

herbie shell --seed 2020089 
(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))))