Average Error: 0.1 → 0.2
Time: 3.0s
Precision: binary64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{1}{\frac{y}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{1}{\frac{y}{\sin y}}
double code(double x, double y) {
	return ((double) (x * (((double) sin(y)) / y)));
}
↓
double code(double x, double y) {
	return ((double) (x * (1.0 / (y / ((double) sin(y))))));
}

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 Error: 0.1 bits

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

  3. Applied clear-numError: 0.2 bits

    \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\]

  4. Final simplificationError: 0.2 bits

    \[\leadsto x \cdot \frac{1}{\frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2020200 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))