Average Error: 0.1 → 0.6
Time: 4.2s
Precision: binary64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z}\right) \cdot \sqrt[3]{\sin y}\right) \cdot \left(\sqrt[3]{z} \cdot \sqrt[3]{\sin y}\right)
(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z)
 :precision binary64
 (-
  (* x (cos y))
  (*
   (* (* (cbrt (* z (sin y))) (cbrt z)) (cbrt (sin y)))
   (* (cbrt z) (cbrt (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 (x * cos(y)) - (((cbrt(z * sin(y)) * cbrt(z)) * cbrt(sin(y))) * (cbrt(z) * cbrt(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_binary640.6

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

  5. Applied cbrt-prod_binary640.6

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

  6. Applied associate-*r*_binary640.6

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

  8. Applied cbrt-prod_binary640.6

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

  9. Final simplification0.6

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

Reproduce

herbie shell --seed 2020233 
(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))))