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

Average Error: 0.1 → 0.6

Time: 8.1s

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 r218575 = x;
        double r218576 = y;
        double r218577 = cos(r218576);
        double r218578 = r218575 * r218577;
        double r218579 = z;
        double r218580 = sin(r218576);
        double r218581 = r218579 * r218580;
        double r218582 = r218578 - r218581;
        return r218582;
}

↓

double f(double x, double y, double z) {
        double r218583 = x;
        double r218584 = y;
        double r218585 = cos(r218584);
        double r218586 = r218583 * r218585;
        double r218587 = z;
        double r218588 = cbrt(r218587);
        double r218589 = r218588 * r218588;
        double r218590 = sin(r218584);
        double r218591 = r218588 * r218590;
        double r218592 = r218589 * r218591;
        double r218593 = r218586 - r218592;
        return r218593;
}

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))))