Average Error: 0.1 → 0.1
Time: 5.1s
Precision: binary64
\[x \cdot \cos y + z \cdot \sin y \]
↓
\[z \cdot \sin y + \cos y \cdot x \]
x \cdot \cos y + z \cdot \sin y
↓
z \cdot \sin y + \cos y \cdot x

(FPCore (x y z) :precision binary64 (+ (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z) :precision binary64 (+ (* z (sin y)) (* (cos y) x)))
double code(double x, double y, double z) {
	return (x * cos(y)) + (z * sin(y));
}
↓
double code(double x, double y, double z) {
	return (z * sin(y)) + (cos(y) * x);
}

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. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)} \]

  3. Taylor expanded in x around 0 0.1

    \[\leadsto \color{blue}{\cos y \cdot x + \sin y \cdot z} \]

  4. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sin y, z, \cos y \cdot x\right)} \]

  5. Applied fma-udef_binary640.1

    \[\leadsto \color{blue}{\sin y \cdot z + \cos y \cdot x} \]

  6. Simplified0.1

    \[\leadsto \color{blue}{z \cdot \sin y} + \cos y \cdot x \]

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2021357 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))