Average Error: 0.1 → 0.4
Time: 5.2s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r239747 = x;
        double r239748 = y;
        double r239749 = cos(r239748);
        double r239750 = r239747 * r239749;
        double r239751 = z;
        double r239752 = sin(r239748);
        double r239753 = r239751 * r239752;
        double r239754 = r239750 - r239753;
        return r239754;
}
↓
double f(double x, double y, double z) {
        double r239755 = x;
        double r239756 = y;
        double r239757 = cos(r239756);
        double r239758 = cbrt(r239757);
        double r239759 = r239758 * r239758;
        double r239760 = r239755 * r239759;
        double r239761 = r239760 * r239758;
        double r239762 = z;
        double r239763 = sin(r239756);
        double r239764 = r239762 * r239763;
        double r239765 = r239761 - r239764;
        return r239765;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2020083 
(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))))