Average Error: 0.1 → 0.6
Time: 16.6s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}
double f(double x, double y, double z) {
        double r156290 = x;
        double r156291 = y;
        double r156292 = cos(r156291);
        double r156293 = r156290 * r156292;
        double r156294 = z;
        double r156295 = sin(r156291);
        double r156296 = r156294 * r156295;
        double r156297 = r156293 + r156296;
        return r156297;
}
↓
double f(double x, double y, double z) {
        double r156298 = x;
        double r156299 = y;
        double r156300 = cos(r156299);
        double r156301 = r156298 * r156300;
        double r156302 = z;
        double r156303 = sin(r156299);
        double r156304 = cbrt(r156303);
        double r156305 = r156304 * r156304;
        double r156306 = r156302 * r156305;
        double r156307 = r156306 * r156304;
        double r156308 = r156301 + r156307;
        return r156308;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

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Results

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Derivation

  1. Initial program 0.1

    \[x \cdot \cos y + z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.6

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

  4. Applied associate-*r*0.6

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

  5. Simplified0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))