Average Error: 0.1 → 0.1
Time: 12.8s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\sin y}{y} \cdot x\]
x \cdot \frac{\sin y}{y}
↓
\frac{\sin y}{y} \cdot x
double f(double x, double y) {
        double r5134845 = x;
        double r5134846 = y;
        double r5134847 = sin(r5134846);
        double r5134848 = r5134847 / r5134846;
        double r5134849 = r5134845 * r5134848;
        return r5134849;
}
↓
double f(double x, double y) {
        double r5134850 = y;
        double r5134851 = sin(r5134850);
        double r5134852 = r5134851 / r5134850;
        double r5134853 = x;
        double r5134854 = r5134852 * r5134853;
        return r5134854;
}

Error

Bits error versus x

Bits error versus y

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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

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))