Average Error: 0.1 → 0.1
Time: 3.2s
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. Applied clear-num_binary640.2

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

  3. Applied pow1_binary640.2

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

  4. Applied pow1_binary640.2

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

  5. Applied pow-prod-down_binary640.2

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2022081 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))