Average Error: 0.1 → 0.5
Time: 15.8s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z \cdot \sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right)\]
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 \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right)
double f(double x, double y, double z) {
        double r148021 = x;
        double r148022 = y;
        double r148023 = cos(r148022);
        double r148024 = r148021 * r148023;
        double r148025 = z;
        double r148026 = sin(r148022);
        double r148027 = r148025 * r148026;
        double r148028 = r148024 + r148027;
        return r148028;
}
↓
double f(double x, double y, double z) {
        double r148029 = x;
        double r148030 = y;
        double r148031 = cos(r148030);
        double r148032 = r148029 * r148031;
        double r148033 = z;
        double r148034 = sin(r148030);
        double r148035 = r148033 * r148034;
        double r148036 = cbrt(r148035);
        double r148037 = r148036 * r148036;
        double r148038 = cbrt(r148033);
        double r148039 = cbrt(r148034);
        double r148040 = r148038 * r148039;
        double r148041 = r148037 * r148040;
        double r148042 = r148032 + r148041;
        return r148042;
}

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

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))