Average Error: 0.1 → 0.1
Time: 2.6s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{\sin y}{y}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r142759 = x;
        double r142760 = y;
        double r142761 = sin(r142760);
        double r142762 = r142761 / r142760;
        double r142763 = r142759 * r142762;
        return r142763;
}
↓
double f(double x, double y) {
        double r142764 = x;
        double r142765 = y;
        double r142766 = sin(r142765);
        double r142767 = r142766 / r142765;
        double r142768 = r142764 * r142767;
        return r142768;
}

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 clear-num0.2

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

  4. Taylor expanded around inf 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020081 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))