Average Error: 0.1 → 0.7
Time: 5.4s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)
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) (z * ((double) (((double) cbrt(((double) sin(y)))) * ((double) cbrt(((double) sin(y)))))))) * ((double) (((double) cbrt(((double) (((double) cbrt(((double) sin(y)))) * ((double) cbrt(((double) sin(y)))))))) * ((double) cbrt(((double) cbrt(((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

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

  4. Applied associate-*r*0.6

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

  6. Applied add-cube-cbrt0.6

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

  7. Applied cbrt-prod0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2020128 
(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))))