Average Error: 0.1 → 0.6
Time: 22.4s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r6635328 = x;
        double r6635329 = y;
        double r6635330 = cos(r6635329);
        double r6635331 = r6635328 * r6635330;
        double r6635332 = z;
        double r6635333 = sin(r6635329);
        double r6635334 = r6635332 * r6635333;
        double r6635335 = r6635331 - r6635334;
        return r6635335;
}
↓
double f(double x, double y, double z) {
        double r6635336 = x;
        double r6635337 = y;
        double r6635338 = cos(r6635337);
        double r6635339 = r6635336 * r6635338;
        double r6635340 = z;
        double r6635341 = cbrt(r6635340);
        double r6635342 = r6635341 * r6635341;
        double r6635343 = sin(r6635337);
        double r6635344 = r6635343 * r6635341;
        double r6635345 = r6635342 * r6635344;
        double r6635346 = r6635339 - r6635345;
        return r6635346;
}

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

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

Reproduce

herbie shell --seed 2019168 +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))))