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 r196652 = x;
        double r196653 = y;
        double r196654 = sin(r196653);
        double r196655 = r196654 / r196653;
        double r196656 = r196652 * r196655;
        return r196656;
}
↓
double f(double x, double y) {
        double r196657 = y;
        double r196658 = sin(r196657);
        double r196659 = r196658 / r196657;
        double r196660 = x;
        double r196661 = r196659 * r196660;
        return r196661;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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 2019350 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))