Average Error: 0.1 → 0.1
Time: 11.3s
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 r124805 = x;
        double r124806 = y;
        double r124807 = sin(r124806);
        double r124808 = r124807 / r124806;
        double r124809 = r124805 * r124808;
        return r124809;
}
↓
double f(double x, double y) {
        double r124810 = y;
        double r124811 = sin(r124810);
        double r124812 = r124811 / r124810;
        double r124813 = x;
        double r124814 = r124812 * r124813;
        return r124814;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.1

    \[x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied *-commutative0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))