Average Error: 0.1 → 0.1
Time: 5.3s
Precision: binary64
\[x \cdot \cos y - z \cdot \sin y \]
↓
\[\cos y \cdot x - z \cdot \sin y \]
x \cdot \cos y - z \cdot \sin y
↓
\cos y \cdot x - z \cdot \sin y

(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z) :precision binary64 (- (* (cos y) x) (* 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 (cos(y) * x) - (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. Applied add-cube-cbrt_binary640.4

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

  3. Applied associate-*r*_binary640.4

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

  4. Applied pow1_binary640.4

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{1}} - z \cdot \sin y \]

  5. Applied pow1_binary640.4

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{1}}\right)\right) \cdot {\left(\sqrt[3]{\cos y}\right)}^{1} - z \cdot \sin y \]

  6. Applied pow1_binary640.4

    \[\leadsto \left(x \cdot \left(\color{blue}{{\left(\sqrt[3]{\cos y}\right)}^{1}} \cdot {\left(\sqrt[3]{\cos y}\right)}^{1}\right)\right) \cdot {\left(\sqrt[3]{\cos y}\right)}^{1} - z \cdot \sin y \]

  7. Applied pow-prod-down_binary640.4

    \[\leadsto \left(x \cdot \color{blue}{{\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)}^{1}}\right) \cdot {\left(\sqrt[3]{\cos y}\right)}^{1} - z \cdot \sin y \]

  8. Applied pow1_binary640.4

    \[\leadsto \left(\color{blue}{{x}^{1}} \cdot {\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)}^{1}\right) \cdot {\left(\sqrt[3]{\cos y}\right)}^{1} - z \cdot \sin y \]

  9. Applied pow-prod-down_binary640.4

    \[\leadsto \color{blue}{{\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right)}^{1}} \cdot {\left(\sqrt[3]{\cos y}\right)}^{1} - z \cdot \sin y \]

  10. Applied pow-prod-down_binary640.4

    \[\leadsto \color{blue}{{\left(\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}\right)}^{1}} - z \cdot \sin y \]

  11. Simplified0.1

    \[\leadsto {\color{blue}{\left(\cos y \cdot x\right)}}^{1} - z \cdot \sin y \]

  12. Final simplification0.1

    \[\leadsto \cos y \cdot x - z \cdot \sin y \]

Reproduce

herbie shell --seed 2021275 
(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))))