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

Average Error: 0.1 → 0.6

Time: 5.7s

Precision: binary64

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 code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) cos(y)))) - ((double) (z * ((double) sin(y))))));
}

↓

double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) cos(y)))) - ((double) (((double) (((double) cbrt(z)) * ((double) cbrt(z)))) * ((double) (((double) cbrt(z)) * ((double) sin(y))))))));
}

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 2020147 
(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))))