Average Error: 0.1 → 0.5
Time: 15.4s
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 r187287 = x;
        double r187288 = y;
        double r187289 = cos(r187288);
        double r187290 = r187287 * r187289;
        double r187291 = z;
        double r187292 = sin(r187288);
        double r187293 = r187291 * r187292;
        double r187294 = r187290 - r187293;
        return r187294;
}
↓
double f(double x, double y, double z) {
        double r187295 = x;
        double r187296 = y;
        double r187297 = cos(r187296);
        double r187298 = r187295 * r187297;
        double r187299 = z;
        double r187300 = sin(r187296);
        double r187301 = r187299 * r187300;
        double r187302 = cbrt(r187301);
        double r187303 = r187302 * r187302;
        double r187304 = cbrt(r187299);
        double r187305 = cbrt(r187300);
        double r187306 = r187304 * r187305;
        double r187307 = r187303 * r187306;
        double r187308 = r187298 - r187307;
        return r187308;
}

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:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))