Average Error: 0.1 → 0.6
Time: 15.3s
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 r203699 = x;
        double r203700 = y;
        double r203701 = cos(r203700);
        double r203702 = r203699 * r203701;
        double r203703 = z;
        double r203704 = sin(r203700);
        double r203705 = r203703 * r203704;
        double r203706 = r203702 - r203705;
        return r203706;
}
↓
double f(double x, double y, double z) {
        double r203707 = x;
        double r203708 = y;
        double r203709 = cos(r203708);
        double r203710 = r203707 * r203709;
        double r203711 = z;
        double r203712 = cbrt(r203711);
        double r203713 = r203712 * r203712;
        double r203714 = sin(r203708);
        double r203715 = r203712 * r203714;
        double r203716 = r203713 * r203715;
        double r203717 = r203710 - r203716;
        return r203717;
}

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 2019351 +o rules:numerics
(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))))