Average Error: 0.1 → 0.6
Time: 5.8s
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 r232406 = x;
        double r232407 = y;
        double r232408 = cos(r232407);
        double r232409 = r232406 * r232408;
        double r232410 = z;
        double r232411 = sin(r232407);
        double r232412 = r232410 * r232411;
        double r232413 = r232409 - r232412;
        return r232413;
}
↓
double f(double x, double y, double z) {
        double r232414 = x;
        double r232415 = y;
        double r232416 = cos(r232415);
        double r232417 = r232414 * r232416;
        double r232418 = z;
        double r232419 = sin(r232415);
        double r232420 = r232418 * r232419;
        double r232421 = cbrt(r232420);
        double r232422 = r232421 * r232421;
        double r232423 = cbrt(r232418);
        double r232424 = cbrt(r232419);
        double r232425 = r232423 * r232424;
        double r232426 = r232422 * r232425;
        double r232427 = r232417 - r232426;
        return r232427;
}

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-prod0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2020036 
(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))))