Average Error: 0.1 → 0.7
Time: 4.3s
Precision: binary64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y}} \cdot {\left(\sqrt[3]{\sqrt[3]{\sin y}}\right)}^{2}\right) + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y}} \cdot {\left(\sqrt[3]{\sqrt[3]{\sin y}}\right)}^{2}\right) + z \cdot \cos y
double code(double x, double y, double z) {
	return ((double) (((double) (x * ((double) sin(y)))) + ((double) (z * ((double) cos(y))))));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (x * ((double) (((double) cbrt(((double) sin(y)))) * ((double) cbrt(((double) sin(y)))))))) * ((double) (((double) cbrt(((double) cbrt(((double) sin(y)))))) * ((double) pow(((double) cbrt(((double) cbrt(((double) sin(y)))))), 2.0)))))) + ((double) (z * ((double) cos(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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.6

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

  4. Applied associate-*r*0.6

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

  6. Applied add-cube-cbrt0.7

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

  7. Simplified0.7

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\color{blue}{{\left(\sqrt[3]{\sqrt[3]{\sin y}}\right)}^{2}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right) + z \cdot \cos y\]

  8. Final simplification0.7

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y}} \cdot {\left(\sqrt[3]{\sqrt[3]{\sin y}}\right)}^{2}\right) + z \cdot \cos y\]

Reproduce

herbie shell --seed 2020196 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))