Average Error: 0.1 → 0.1
Time: 7.0s
Precision: binary64
\[x \cdot \cos y - z \cdot \sin y \]
↓
\[x \cdot \cos y - \sin y \cdot z \]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \sin y \cdot z

(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* z (sin y))))
↓
(FPCore (x y z) :precision binary64 (- (* x (cos y)) (* (sin y) z)))
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)) - (sin(y) * z);
}

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 *-un-lft-identity_binary640.1

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

  3. Applied associate-*l*_binary640.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2022096 
(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))))