Average Error: 0.1 → 1.4
Time: 5.1s
Precision: binary64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\sqrt[3]{x \cdot \cos y - z \cdot \sin y} \cdot \left(\sqrt[3]{x \cdot \cos y - z \cdot \sin y} \cdot \sqrt[3]{x \cdot \cos y - z \cdot \sin y}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
\sqrt[3]{x \cdot \cos y - z \cdot \sin y} \cdot \left(\sqrt[3]{x \cdot \cos y - z \cdot \sin y} \cdot \sqrt[3]{x \cdot \cos y - z \cdot \sin y}\right)
(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z)
 :precision binary64
 (*
  (cbrt (- (* x (cos y)) (* z (sin y))))
  (*
   (cbrt (- (* x (cos y)) (* z (sin y))))
   (cbrt (- (* x (cos y)) (* z (sin y)))))))
double code(double x, double y, double z) {
	return (x * cos(y)) - (z * sin(y));
}
↓
double code(double x, double y, double z) {
	return cbrt((x * cos(y)) - (z * sin(y))) * (cbrt((x * cos(y)) - (z * sin(y))) * cbrt((x * cos(y)) - (z * 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-cbrt_binary64_81971.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020281 
(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))))