Average Error: 0.1 → 0.6
Time: 1.0m
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sin y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\left(\sqrt[3]{\sqrt[3]{z}} \cdot \sqrt[3]{\sqrt[3]{z} \cdot \sqrt[3]{z}}\right) \cdot \sin y\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r10175348 = x;
        double r10175349 = y;
        double r10175350 = cos(r10175349);
        double r10175351 = r10175348 * r10175350;
        double r10175352 = z;
        double r10175353 = sin(r10175349);
        double r10175354 = r10175352 * r10175353;
        double r10175355 = r10175351 - r10175354;
        return r10175355;
}
↓
double f(double x, double y, double z) {
        double r10175356 = x;
        double r10175357 = y;
        double r10175358 = cos(r10175357);
        double r10175359 = r10175356 * r10175358;
        double r10175360 = z;
        double r10175361 = cbrt(r10175360);
        double r10175362 = cbrt(r10175361);
        double r10175363 = r10175361 * r10175361;
        double r10175364 = cbrt(r10175363);
        double r10175365 = r10175362 * r10175364;
        double r10175366 = sin(r10175357);
        double r10175367 = r10175365 * r10175366;
        double r10175368 = r10175367 * r10175363;
        double r10175369 = r10175359 - r10175368;
        return r10175369;
}

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. Using strategy rm

  6. Applied add-cube-cbrt0.6

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

  7. Applied cbrt-prod0.6

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

  8. Final simplification0.6

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))