Average Error: 0.1 → 0.6
Time: 17.8s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \sqrt[3]{\sin y} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot z\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \sqrt[3]{\sin y} \cdot \left(\left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right) \cdot z\right)
double f(double x, double y, double z) {
        double r6914326 = x;
        double r6914327 = y;
        double r6914328 = cos(r6914327);
        double r6914329 = r6914326 * r6914328;
        double r6914330 = z;
        double r6914331 = sin(r6914327);
        double r6914332 = r6914330 * r6914331;
        double r6914333 = r6914329 - r6914332;
        return r6914333;
}
↓
double f(double x, double y, double z) {
        double r6914334 = x;
        double r6914335 = y;
        double r6914336 = cos(r6914335);
        double r6914337 = r6914334 * r6914336;
        double r6914338 = sin(r6914335);
        double r6914339 = cbrt(r6914338);
        double r6914340 = r6914339 * r6914339;
        double r6914341 = z;
        double r6914342 = r6914340 * r6914341;
        double r6914343 = r6914339 * r6914342;
        double r6914344 = r6914337 - r6914343;
        return r6914344;
}

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

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

  4. Applied associate-*r*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019158 +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))))