Average Error: 0.1 → 0.2
Time: 3.5s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \left(\sin y \cdot \frac{1}{y}\right)\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \left(\sin y \cdot \frac{1}{y}\right)
double f(double x, double y) {
        double r122266 = x;
        double r122267 = y;
        double r122268 = sin(r122267);
        double r122269 = r122268 / r122267;
        double r122270 = r122266 * r122269;
        return r122270;
}
↓
double f(double x, double y) {
        double r122271 = x;
        double r122272 = y;
        double r122273 = sin(r122272);
        double r122274 = 1.0;
        double r122275 = r122274 / r122272;
        double r122276 = r122273 * r122275;
        double r122277 = r122271 * r122276;
        return r122277;
}

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 div-inv0.2

    \[\leadsto x \cdot \color{blue}{\left(\sin y \cdot \frac{1}{y}\right)}\]

  4. Final simplification0.2

    \[\leadsto x \cdot \left(\sin y \cdot \frac{1}{y}\right)\]

Reproduce

herbie shell --seed 2020039 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))