Average Error: 0.1 → 0.2
Time: 10.6s
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 r156305 = x;
        double r156306 = y;
        double r156307 = sin(r156306);
        double r156308 = r156307 / r156306;
        double r156309 = r156305 * r156308;
        return r156309;
}
↓
double f(double x, double y) {
        double r156310 = x;
        double r156311 = 1.0;
        double r156312 = y;
        double r156313 = sin(r156312);
        double r156314 = r156312 / r156313;
        double r156315 = r156311 / r156314;
        double r156316 = r156310 * r156315;
        return r156316;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))