Average Error: 0.1 → 0.6
Time: 10.8s
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 r173832 = x;
        double r173833 = y;
        double r173834 = cos(r173833);
        double r173835 = r173832 * r173834;
        double r173836 = z;
        double r173837 = sin(r173833);
        double r173838 = r173836 * r173837;
        double r173839 = r173835 - r173838;
        return r173839;
}
↓
double f(double x, double y, double z) {
        double r173840 = x;
        double r173841 = y;
        double r173842 = cos(r173841);
        double r173843 = r173840 * r173842;
        double r173844 = z;
        double r173845 = cbrt(r173844);
        double r173846 = r173845 * r173845;
        double r173847 = sin(r173841);
        double r173848 = r173845 * r173847;
        double r173849 = r173846 * r173848;
        double r173850 = r173843 - r173849;
        return r173850;
}

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 1978988140 
(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))))