Average Error: 0.1 → 0.4
Time: 5.1s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r157268 = x;
        double r157269 = y;
        double r157270 = cos(r157269);
        double r157271 = r157268 * r157270;
        double r157272 = z;
        double r157273 = sin(r157269);
        double r157274 = r157272 * r157273;
        double r157275 = r157271 + r157274;
        return r157275;
}
↓
double f(double x, double y, double z) {
        double r157276 = x;
        double r157277 = y;
        double r157278 = cos(r157277);
        double r157279 = cbrt(r157278);
        double r157280 = r157279 * r157279;
        double r157281 = cbrt(r157280);
        double r157282 = cbrt(r157279);
        double r157283 = r157281 * r157282;
        double r157284 = r157283 * r157279;
        double r157285 = r157276 * r157284;
        double r157286 = r157285 * r157279;
        double r157287 = z;
        double r157288 = sin(r157277);
        double r157289 = r157287 * r157288;
        double r157290 = r157286 + r157289;
        return r157290;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied add-cube-cbrt0.4

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

  7. Applied cbrt-prod0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2020056 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))