Average Error: 0.1 → 0.3
Time: 18.0s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{1}{\frac{1}{\sin y} \cdot y}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{1}{\frac{1}{\sin y} \cdot y}
double f(double x, double y) {
        double r153511 = x;
        double r153512 = y;
        double r153513 = sin(r153512);
        double r153514 = r153513 / r153512;
        double r153515 = r153511 * r153514;
        return r153515;
}
↓
double f(double x, double y) {
        double r153516 = x;
        double r153517 = 1.0;
        double r153518 = y;
        double r153519 = sin(r153518);
        double r153520 = r153517 / r153519;
        double r153521 = r153520 * r153518;
        double r153522 = r153517 / r153521;
        double r153523 = r153516 * r153522;
        return r153523;
}

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. Using strategy rm

  5. Applied div-inv0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))