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

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

  4. Final simplificationError: 0.2 bits

    \[\leadsto x \cdot \left(\sin y \cdot \frac{1}{y}\right)\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))