Average Error: 0.1 → 0.2
Time: 5.3s
Precision: binary64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt[3]{{\cos y}^{6}}\right)}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt[3]{{\cos y}^{6}}\right)}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
(FPCore (x y z) :precision binary64 (+ (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z)
 :precision binary64
 (+
  (* (* x (pow (cbrt (pow (cos y) 6.0)) 0.3333333333333333)) (cbrt (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 ((x * pow(cbrt(pow(cos(y), 6.0)), 0.3333333333333333)) * cbrt(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_binary640.4

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

  4. Applied associate-*r*_binary640.4

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

  6. Applied pow1/3_binary6415.7

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\cos y}^{0.3333333333333333}}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  7. Applied pow1/3_binary6415.6

    \[\leadsto \left(x \cdot \left(\color{blue}{{\cos y}^{0.3333333333333333}} \cdot {\cos y}^{0.3333333333333333}\right)\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  8. Applied pow-prod-down_binary640.2

    \[\leadsto \left(x \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{0.3333333333333333}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
  9. Using strategy rm

  10. Applied add-cbrt-cube_binary640.2

    \[\leadsto \left(x \cdot {\color{blue}{\left(\sqrt[3]{\left(\left(\cos y \cdot \cos y\right) \cdot \left(\cos y \cdot \cos y\right)\right) \cdot \left(\cos y \cdot \cos y\right)}\right)}}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  11. Simplified0.2

    \[\leadsto \left(x \cdot {\left(\sqrt[3]{\color{blue}{{\cos y}^{6}}}\right)}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  12. Final simplification0.2

    \[\leadsto \left(x \cdot {\left(\sqrt[3]{{\cos y}^{6}}\right)}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

Reproduce

herbie shell --seed 2020288 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))