Average Error: 0.1 → 0.1
Time: 13.6s
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 r4816633 = x;
        double r4816634 = y;
        double r4816635 = sin(r4816634);
        double r4816636 = r4816635 / r4816634;
        double r4816637 = r4816633 * r4816636;
        return r4816637;
}
↓
double f(double x, double y) {
        double r4816638 = y;
        double r4816639 = sin(r4816638);
        double r4816640 = r4816639 / r4816638;
        double r4816641 = x;
        double r4816642 = r4816640 * r4816641;
        return r4816642;
}

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 2019169 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))