Average Error: 0.1 → 0.2
Time: 3.4s
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 r103929 = x;
        double r103930 = y;
        double r103931 = sin(r103930);
        double r103932 = r103931 / r103930;
        double r103933 = r103929 * r103932;
        return r103933;
}
↓
double f(double x, double y) {
        double r103934 = x;
        double r103935 = 1.0;
        double r103936 = y;
        double r103937 = sin(r103936);
        double r103938 = r103936 / r103937;
        double r103939 = r103935 / r103938;
        double r103940 = r103934 * r103939;
        return r103940;
}

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 2020001 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))