Average Error: 0.1 → 0.7
Time: 5.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(z \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}\right) \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\right) \cdot \sqrt[3]{\sin y}\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(z \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}}\right) \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\right) \cdot \sqrt[3]{\sin y}
double f(double x, double y, double z) {
        double r210274 = x;
        double r210275 = y;
        double r210276 = cos(r210275);
        double r210277 = r210274 * r210276;
        double r210278 = z;
        double r210279 = sin(r210275);
        double r210280 = r210278 * r210279;
        double r210281 = r210277 + r210280;
        return r210281;
}
↓
double f(double x, double y, double z) {
        double r210282 = x;
        double r210283 = y;
        double r210284 = cos(r210283);
        double r210285 = r210282 * r210284;
        double r210286 = z;
        double r210287 = sin(r210283);
        double r210288 = cbrt(r210287);
        double r210289 = r210288 * r210288;
        double r210290 = cbrt(r210289);
        double r210291 = r210288 * r210290;
        double r210292 = cbrt(r210288);
        double r210293 = r210291 * r210292;
        double r210294 = r210286 * r210293;
        double r210295 = r210294 * r210288;
        double r210296 = r210285 + r210295;
        return r210296;
}

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

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

  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. Using strategy rm

  6. Applied add-cube-cbrt0.6

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

  7. Applied cbrt-prod0.7

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

  8. Applied associate-*r*0.7

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

  9. Final simplification0.7

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

Reproduce

herbie shell --seed 2020064 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))