Average Error: 0.1 → 0.5
Time: 25.0s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{z \cdot \sin y}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r187236 = x;
        double r187237 = y;
        double r187238 = cos(r187237);
        double r187239 = r187236 * r187238;
        double r187240 = z;
        double r187241 = sin(r187237);
        double r187242 = r187240 * r187241;
        double r187243 = r187239 + r187242;
        return r187243;
}
↓
double f(double x, double y, double z) {
        double r187244 = x;
        double r187245 = y;
        double r187246 = cos(r187245);
        double r187247 = r187244 * r187246;
        double r187248 = z;
        double r187249 = cbrt(r187248);
        double r187250 = sin(r187245);
        double r187251 = cbrt(r187250);
        double r187252 = r187248 * r187250;
        double r187253 = cbrt(r187252);
        double r187254 = r187251 * r187253;
        double r187255 = r187249 * r187254;
        double r187256 = r187255 * r187253;
        double r187257 = r187247 + r187256;
        return r187257;
}

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

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

  6. Applied associate-*l*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))