Average Error: 0.1 → 0.6
Time: 5.4s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{\sin y}
double f(double x, double y, double z) {
        double r223965 = x;
        double r223966 = y;
        double r223967 = cos(r223966);
        double r223968 = r223965 * r223967;
        double r223969 = z;
        double r223970 = sin(r223966);
        double r223971 = r223969 * r223970;
        double r223972 = r223968 - r223971;
        return r223972;
}
↓
double f(double x, double y, double z) {
        double r223973 = x;
        double r223974 = y;
        double r223975 = cos(r223974);
        double r223976 = r223973 * r223975;
        double r223977 = z;
        double r223978 = sin(r223974);
        double r223979 = cbrt(r223978);
        double r223980 = r223979 * r223979;
        double r223981 = r223977 * r223980;
        double r223982 = r223981 * r223979;
        double r223983 = r223976 - r223982;
        return r223983;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2020064 
(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))))