Average Error: 0.1 → 0.5
Time: 8.9s
Precision: binary64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{\sin y}\right) \cdot \sqrt[3]{z \cdot \sin y}
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) (((double) cbrt(((double) (z * ((double) sin(y)))))) * ((double) cbrt(z)))) * ((double) cbrt(((double) sin(y)))))) * ((double) cbrt(((double) (z * ((double) sin(y))))))))));
}

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

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

  5. Applied cbrt-prod0.5

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

  6. Applied associate-*r*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2020163 
(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))))