Average Error: 0.1 → 0.2
Time: 3.3s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{1}{\frac{y}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{1}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r103732 = x;
        double r103733 = y;
        double r103734 = sin(r103733);
        double r103735 = r103734 / r103733;
        double r103736 = r103732 * r103735;
        return r103736;
}
↓
double f(double x, double y) {
        double r103737 = x;
        double r103738 = 1.0;
        double r103739 = y;
        double r103740 = sin(r103739);
        double r103741 = r103739 / r103740;
        double r103742 = r103738 / r103741;
        double r103743 = r103737 * r103742;
        return r103743;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020056 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))