Average Error: 0.1 → 0.1
Time: 13.3s
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 r3249583 = x;
        double r3249584 = y;
        double r3249585 = sin(r3249584);
        double r3249586 = r3249585 / r3249584;
        double r3249587 = r3249583 * r3249586;
        return r3249587;
}
↓
double f(double x, double y) {
        double r3249588 = y;
        double r3249589 = sin(r3249588);
        double r3249590 = r3249589 / r3249588;
        double r3249591 = x;
        double r3249592 = r3249590 * r3249591;
        return r3249592;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))