Average Error: 0.1 → 0.1
Time: 3.4s
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 r114488 = x;
        double r114489 = y;
        double r114490 = sin(r114489);
        double r114491 = r114490 / r114489;
        double r114492 = r114488 * r114491;
        return r114492;
}
↓
double f(double x, double y) {
        double r114493 = y;
        double r114494 = sin(r114493);
        double r114495 = r114494 / r114493;
        double r114496 = x;
        double r114497 = r114495 * r114496;
        return r114497;
}

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 2020062 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))