Average Error: 0.1 → 0.9
Time: 5.3s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{x \cdot \cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{x \cdot \cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r201964 = x;
        double r201965 = y;
        double r201966 = cos(r201965);
        double r201967 = r201964 * r201966;
        double r201968 = z;
        double r201969 = sin(r201965);
        double r201970 = r201968 * r201969;
        double r201971 = r201967 + r201970;
        return r201971;
}
↓
double f(double x, double y, double z) {
        double r201972 = x;
        double r201973 = y;
        double r201974 = cos(r201973);
        double r201975 = r201972 * r201974;
        double r201976 = cbrt(r201975);
        double r201977 = cbrt(r201972);
        double r201978 = r201976 * r201977;
        double r201979 = cbrt(r201974);
        double r201980 = r201978 * r201979;
        double r201981 = r201980 * r201976;
        double r201982 = z;
        double r201983 = sin(r201973);
        double r201984 = r201982 * r201983;
        double r201985 = r201981 + r201984;
        return r201985;
}

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. Using strategy rm

  5. Applied cbrt-prod0.9

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

  6. Applied associate-*r*0.9

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

  7. Final simplification0.9

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

Reproduce

herbie shell --seed 2020018 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))