Average Error: 0.1 → 0.2
Time: 3.2s
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 r159683 = x;
        double r159684 = y;
        double r159685 = sin(r159684);
        double r159686 = r159685 / r159684;
        double r159687 = r159683 * r159686;
        return r159687;
}
↓
double f(double x, double y) {
        double r159688 = x;
        double r159689 = 1.0;
        double r159690 = y;
        double r159691 = sin(r159690);
        double r159692 = r159690 / r159691;
        double r159693 = r159689 / r159692;
        double r159694 = r159688 * r159693;
        return r159694;
}

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 2020018 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))