Average Error: 0.1 → 0.3
Time: 21.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(\sqrt[3]{\cos y \cdot \cos y} \cdot x\right) \cdot \sqrt[3]{\cos y} - \sin y \cdot z\]
x \cdot \cos y - z \cdot \sin y
↓
\left(\sqrt[3]{\cos y \cdot \cos y} \cdot x\right) \cdot \sqrt[3]{\cos y} - \sin y \cdot z
double f(double x, double y, double z) {
        double r9906390 = x;
        double r9906391 = y;
        double r9906392 = cos(r9906391);
        double r9906393 = r9906390 * r9906392;
        double r9906394 = z;
        double r9906395 = sin(r9906391);
        double r9906396 = r9906394 * r9906395;
        double r9906397 = r9906393 - r9906396;
        return r9906397;
}
↓
double f(double x, double y, double z) {
        double r9906398 = y;
        double r9906399 = cos(r9906398);
        double r9906400 = r9906399 * r9906399;
        double r9906401 = cbrt(r9906400);
        double r9906402 = x;
        double r9906403 = r9906401 * r9906402;
        double r9906404 = cbrt(r9906399);
        double r9906405 = r9906403 * r9906404;
        double r9906406 = sin(r9906398);
        double r9906407 = z;
        double r9906408 = r9906406 * r9906407;
        double r9906409 = r9906405 - r9906408;
        return r9906409;
}

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. Using strategy rm

  6. Applied cbrt-unprod0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019164 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))