Average Error: 0.1 → 0.6
Time: 43.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r10126148 = x;
        double r10126149 = y;
        double r10126150 = cos(r10126149);
        double r10126151 = r10126148 * r10126150;
        double r10126152 = z;
        double r10126153 = sin(r10126149);
        double r10126154 = r10126152 * r10126153;
        double r10126155 = r10126151 - r10126154;
        return r10126155;
}
↓
double f(double x, double y, double z) {
        double r10126156 = x;
        double r10126157 = y;
        double r10126158 = cos(r10126157);
        double r10126159 = r10126156 * r10126158;
        double r10126160 = z;
        double r10126161 = cbrt(r10126160);
        double r10126162 = r10126161 * r10126161;
        double r10126163 = sin(r10126157);
        double r10126164 = r10126163 * r10126161;
        double r10126165 = r10126162 * r10126164;
        double r10126166 = r10126159 - r10126165;
        return r10126166;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))