Average Error: 0.1 → 0.9
Time: 5.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \cos y\right)
double code(double x, double y, double z) {
	return ((x * sin(y)) + (z * cos(y)));
}
↓
double code(double x, double y, double z) {
	return ((x * sin(y)) + ((cbrt(z) * cbrt(z)) * (cbrt(z) * 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-cbrt0.9

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

  4. Applied associate-*l*0.9

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

  5. Final simplification0.9

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

Reproduce

herbie shell --seed 2020060 
(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))))