Average Error: 0.1 → 0.9
Time: 5.9s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x \cdot \cos y}\right) \cdot \sqrt[3]{x \cdot \cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x \cdot \cos y}\right) \cdot \sqrt[3]{x \cdot \cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r194917 = x;
        double r194918 = y;
        double r194919 = cos(r194918);
        double r194920 = r194917 * r194919;
        double r194921 = z;
        double r194922 = sin(r194918);
        double r194923 = r194921 * r194922;
        double r194924 = r194920 + r194923;
        return r194924;
}
↓
double f(double x, double y, double z) {
        double r194925 = x;
        double r194926 = y;
        double r194927 = cos(r194926);
        double r194928 = r194925 * r194927;
        double r194929 = cbrt(r194928);
        double r194930 = r194929 * r194929;
        double r194931 = r194930 * r194929;
        double r194932 = z;
        double r194933 = sin(r194926);
        double r194934 = r194932 * r194933;
        double r194935 = r194931 + r194934;
        return r194935;
}

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-cbrt0.9

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

  4. Final simplification0.9

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

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))