Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A

Average Error: 0.1 → 0.6

Time: 5.5s

Precision: 64

Math

\[x \cdot \cos y - z \cdot \sin y\]

↓

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

C

double f(double x, double y, double z) {
        double r241913 = x;
        double r241914 = y;
        double r241915 = cos(r241914);
        double r241916 = r241913 * r241915;
        double r241917 = z;
        double r241918 = sin(r241914);
        double r241919 = r241917 * r241918;
        double r241920 = r241916 - r241919;
        return r241920;
}

↓

double f(double x, double y, double z) {
        double r241921 = x;
        double r241922 = y;
        double r241923 = cos(r241922);
        double r241924 = r241921 * r241923;
        double r241925 = z;
        double r241926 = cbrt(r241925);
        double r241927 = r241926 * r241926;
        double r241928 = sin(r241922);
        double r241929 = r241926 * r241928;
        double r241930 = r241927 * r241929;
        double r241931 = r241924 - r241930;
        return r241931;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

1. Initial program 0.1

   \[x \cdot \cos y - z \cdot \sin y\]
2. Using strategy rm

3. Applied add-cube-cbrt 0.6

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

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 simplification 0.6

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

Reproduce

herbie shell --seed 2019356 
(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))))