Average Error: 0.1 → 0.4
Time: 21.4s
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 r10593823 = x;
        double r10593824 = y;
        double r10593825 = cos(r10593824);
        double r10593826 = r10593823 * r10593825;
        double r10593827 = z;
        double r10593828 = sin(r10593824);
        double r10593829 = r10593827 * r10593828;
        double r10593830 = r10593826 - r10593829;
        return r10593830;
}
↓
double f(double x, double y, double z) {
        double r10593831 = z;
        double r10593832 = -r10593831;
        double r10593833 = y;
        double r10593834 = sin(r10593833);
        double r10593835 = r10593832 * r10593834;
        double r10593836 = cos(r10593833);
        double r10593837 = cbrt(r10593836);
        double r10593838 = r10593837 * r10593837;
        double r10593839 = x;
        double r10593840 = r10593838 * r10593839;
        double r10593841 = r10593837 * r10593840;
        double r10593842 = r10593835 + r10593841;
        return r10593842;
}

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