Average Error: 0.1 → 0.6
Time: 5.7s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z \cdot \sin y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z \cdot \sin y} \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r223324 = x;
        double r223325 = y;
        double r223326 = cos(r223325);
        double r223327 = r223324 * r223326;
        double r223328 = z;
        double r223329 = sin(r223325);
        double r223330 = r223328 * r223329;
        double r223331 = r223327 - r223330;
        return r223331;
}
↓
double f(double x, double y, double z) {
        double r223332 = x;
        double r223333 = y;
        double r223334 = cos(r223333);
        double r223335 = r223332 * r223334;
        double r223336 = z;
        double r223337 = sin(r223333);
        double r223338 = r223336 * r223337;
        double r223339 = cbrt(r223338);
        double r223340 = cbrt(r223336);
        double r223341 = cbrt(r223337);
        double r223342 = r223340 * r223341;
        double r223343 = r223339 * r223342;
        double r223344 = r223343 * r223339;
        double r223345 = r223335 - r223344;
        return r223345;
}

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

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

  6. Final simplification0.6

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

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))))