Average Error: 0.1 → 0.2
Time: 3.1s
Precision: binary64
\[x \cdot \frac{\sin y}{y} \]
↓
\[\frac{x}{\frac{1}{\frac{\sin y}{y}}} \]
x \cdot \frac{\sin y}{y}
↓
\frac{x}{\frac{1}{\frac{\sin y}{y}}}

(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))
↓
(FPCore (x y) :precision binary64 (/ x (/ 1.0 (/ (sin y) y))))
double code(double x, double y) {
	return x * (sin(y) / y);
}
↓
double code(double x, double y) {
	return x / (1.0 / (sin(y) / 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 0.1

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

  2. Applied clear-num_binary640.2

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

  3. Applied un-div-inv_binary640.1

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

  4. Applied clear-num_binary640.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2021275 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))