Average Error: 0.1 → 0.6
Time: 50.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sin y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sin y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r8774865 = x;
        double r8774866 = y;
        double r8774867 = cos(r8774866);
        double r8774868 = r8774865 * r8774867;
        double r8774869 = z;
        double r8774870 = sin(r8774866);
        double r8774871 = r8774869 * r8774870;
        double r8774872 = r8774868 - r8774871;
        return r8774872;
}
↓
double f(double x, double y, double z) {
        double r8774873 = x;
        double r8774874 = y;
        double r8774875 = cos(r8774874);
        double r8774876 = r8774873 * r8774875;
        double r8774877 = z;
        double r8774878 = cbrt(r8774877);
        double r8774879 = cbrt(r8774878);
        double r8774880 = r8774878 * r8774878;
        double r8774881 = cbrt(r8774880);
        double r8774882 = r8774879 * r8774881;
        double r8774883 = sin(r8774874);
        double r8774884 = r8774882 * r8774883;
        double r8774885 = r8774884 * r8774880;
        double r8774886 = r8774876 - r8774885;
        return r8774886;
}

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-cbrt0.6

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

  4. Applied associate-*l*0.6

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

  6. Applied add-cube-cbrt0.6

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

  7. Applied cbrt-prod0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))