Average Error: 0.1 → 0.1
Time: 2.7s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{\sin y}{y}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r167263 = x;
        double r167264 = y;
        double r167265 = sin(r167264);
        double r167266 = r167265 / r167264;
        double r167267 = r167263 * r167266;
        return r167267;
}
↓
double f(double x, double y) {
        double r167268 = x;
        double r167269 = y;
        double r167270 = sin(r167269);
        double r167271 = r167270 / r167269;
        double r167272 = r167268 * r167271;
        return r167272;
}

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. Taylor expanded around inf 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020081 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))