Average Error: 0.1 → 0.6
Time: 5.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r194064 = x;
        double r194065 = y;
        double r194066 = cos(r194065);
        double r194067 = r194064 * r194066;
        double r194068 = z;
        double r194069 = sin(r194065);
        double r194070 = r194068 * r194069;
        double r194071 = r194067 - r194070;
        return r194071;
}
↓
double f(double x, double y, double z) {
        double r194072 = x;
        double r194073 = y;
        double r194074 = cos(r194073);
        double r194075 = r194072 * r194074;
        double r194076 = z;
        double r194077 = cbrt(r194076);
        double r194078 = r194077 * r194077;
        double r194079 = sin(r194073);
        double r194080 = r194077 * r194079;
        double r194081 = r194078 * r194080;
        double r194082 = r194075 - r194081;
        return r194082;
}

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

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))