Average Error: 0.1 → 0.4
Time: 22.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(-z\right) \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot x\right)\]
x \cdot \cos y - z \cdot \sin y
↓
\left(-z\right) \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot x\right)
double f(double x, double y, double z) {
        double r6983973 = x;
        double r6983974 = y;
        double r6983975 = cos(r6983974);
        double r6983976 = r6983973 * r6983975;
        double r6983977 = z;
        double r6983978 = sin(r6983974);
        double r6983979 = r6983977 * r6983978;
        double r6983980 = r6983976 - r6983979;
        return r6983980;
}
↓
double f(double x, double y, double z) {
        double r6983981 = z;
        double r6983982 = -r6983981;
        double r6983983 = y;
        double r6983984 = sin(r6983983);
        double r6983985 = r6983982 * r6983984;
        double r6983986 = cos(r6983983);
        double r6983987 = cbrt(r6983986);
        double r6983988 = r6983987 * r6983987;
        double r6983989 = x;
        double r6983990 = r6983988 * r6983989;
        double r6983991 = r6983987 * r6983990;
        double r6983992 = r6983985 + r6983991;
        return r6983992;
}

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 sub-neg0.1

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

  5. Applied add-cube-cbrt0.4

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

  6. Applied associate-*r*0.4

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

  7. Final simplification0.4

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))