Average Error: 0.1 → 0.6
Time: 23.0s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \sqrt[3]{\sin y \cdot z} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\right)
double f(double x, double y, double z) {
        double r9671963 = x;
        double r9671964 = y;
        double r9671965 = cos(r9671964);
        double r9671966 = r9671963 * r9671965;
        double r9671967 = z;
        double r9671968 = sin(r9671964);
        double r9671969 = r9671967 * r9671968;
        double r9671970 = r9671966 - r9671969;
        return r9671970;
}
↓
double f(double x, double y, double z) {
        double r9671971 = x;
        double r9671972 = y;
        double r9671973 = cos(r9671972);
        double r9671974 = r9671971 * r9671973;
        double r9671975 = sin(r9671972);
        double r9671976 = z;
        double r9671977 = r9671975 * r9671976;
        double r9671978 = cbrt(r9671977);
        double r9671979 = cbrt(r9671975);
        double r9671980 = r9671979 * r9671979;
        double r9671981 = cbrt(r9671976);
        double r9671982 = r9671981 * r9671981;
        double r9671983 = r9671980 * r9671982;
        double r9671984 = r9671978 * r9671983;
        double r9671985 = r9671974 - r9671984;
        return r9671985;
}

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

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

  5. Applied cbrt-prod0.5

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

  6. Applied cbrt-prod0.6

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

  7. Applied swap-sqr0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019162 +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))))