Average Error: 0.1 → 0.1
Time: 3.9s
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. Using strategy rm

  3. Applied *-commutative_binary640.1

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

  4. Final simplification0.1

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

Alternatives

Reproduce

herbie shell --seed 2021118 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))