Average Error: 0.1 → 0.6
Time: 15.8s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r163131 = x;
        double r163132 = y;
        double r163133 = cos(r163132);
        double r163134 = r163131 * r163133;
        double r163135 = z;
        double r163136 = sin(r163132);
        double r163137 = r163135 * r163136;
        double r163138 = r163134 - r163137;
        return r163138;
}
↓
double f(double x, double y, double z) {
        double r163139 = x;
        double r163140 = y;
        double r163141 = cos(r163140);
        double r163142 = r163139 * r163141;
        double r163143 = z;
        double r163144 = sin(r163140);
        double r163145 = r163143 * r163144;
        double r163146 = cbrt(r163145);
        double r163147 = r163146 * r163146;
        double r163148 = r163147 * r163146;
        double r163149 = r163142 - r163148;
        return r163149;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019297 
(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))))