Average Error: 0.1 → 0.2
Time: 4.1s
Precision: binary64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\cos y}^{2}\right)}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\cos y}^{2}\right)}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y}
(FPCore (x y z) :precision binary64 (+ (* x (sin y)) (* z (cos y))))
↓
(FPCore (x y z)
 :precision binary64
 (+
  (* x (sin y))
  (* (* z (pow (pow (cos y) 2.0) 0.3333333333333333)) (cbrt (cos y)))))
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)) + ((z * pow(pow(cos(y), 2.0), 0.3333333333333333)) * cbrt(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-cbrt_binary640.4

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

  4. Applied associate-*r*_binary640.4

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

  6. Applied pow1/3_binary6416.9

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

  7. Applied pow1/3_binary6416.8

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

  8. Applied pow-prod-down_binary640.2

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

  9. Simplified0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot {\color{blue}{\left({\cos y}^{2}\right)}}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y}\]

  10. Final simplification0.2

    \[\leadsto x \cdot \sin y + \left(z \cdot {\left({\cos y}^{2}\right)}^{0.3333333333333333}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2020233 
(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))))