Average Error: 0.1 → 0.5
Time: 5.2s
Precision: binary64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left({\left(\sqrt[3]{\sqrt[3]{\cos y}}\right)}^{4} \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left({\left(\sqrt[3]{\sqrt[3]{\cos y}}\right)}^{4} \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right)\right) \cdot \sqrt[3]{\cos y} - 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) (((double) (x * ((double) (((double) pow(((double) cbrt(((double) cbrt(((double) cos(y)))))), 4.0)) * ((double) (((double) cbrt(((double) cbrt(((double) cos(y)))))) * ((double) cbrt(((double) cbrt(((double) cos(y)))))))))))) * ((double) cbrt(((double) cos(y)))))) - ((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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied add-cube-cbrt0.4

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

  7. Applied add-cube-cbrt0.5

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

  8. Applied swap-sqr0.5

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

  9. Simplified0.5

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

  10. Final simplification0.5

    \[\leadsto \left(x \cdot \left({\left(\sqrt[3]{\sqrt[3]{\cos y}}\right)}^{4} \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

Reproduce

herbie shell --seed 2020173 
(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))))