Average Error: 0.1 → 0.1
Time: 8.6s
Precision: binary64
\[x \cdot \cos y - z \cdot \sin y \]
↓
\[x \cdot \cos y - z \cdot \sin y \]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \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 (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 * 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. Applied add-cube-cbrt_binary640.6

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

  3. Applied pow1/3_binary6429.0

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

  4. Applied pow1/3_binary6429.2

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

  5. Applied pow1/3_binary6429.3

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

  6. Applied pow-sqr_binary6429.3

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

  7. Applied pow-prod-up_binary640.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2022088 
(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))))