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

Average Error: 0.1 → 0.6

Time: 24.5s

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 r146500 = x;
        double r146501 = y;
        double r146502 = cos(r146501);
        double r146503 = r146500 * r146502;
        double r146504 = z;
        double r146505 = sin(r146501);
        double r146506 = r146504 * r146505;
        double r146507 = r146503 - r146506;
        return r146507;
}

↓

double f(double x, double y, double z) {
        double r146508 = x;
        double r146509 = y;
        double r146510 = cos(r146509);
        double r146511 = r146508 * r146510;
        double r146512 = z;
        double r146513 = cbrt(r146512);
        double r146514 = r146513 * r146513;
        double r146515 = sin(r146509);
        double r146516 = r146513 * r146515;
        double r146517 = r146514 * r146516;
        double r146518 = r146511 - r146517;
        return r146518;
}

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 2019322 
(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))))