Average Error: 0.1 → 0.1
Time: 2.6s
Precision: binary64
\[x \cdot \frac{\sin y}{y} \]
↓
\[\frac{\sin y}{y} \cdot x \]
x \cdot \frac{\sin y}{y}
↓
\frac{\sin y}{y} \cdot x

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

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \frac{\sin y}{y} \]
  2. Using strategy rm

  3. Applied *-commutative_binary640.1

    \[\leadsto \color{blue}{\frac{\sin y}{y} \cdot x} \]

  4. Final simplification0.1

    \[\leadsto \frac{\sin y}{y} \cdot x \]

Reproduce

herbie shell --seed 2021204 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))