Average Error: 0.1 → 0.1
Time: 10.2s
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 r173743 = x;
        double r173744 = y;
        double r173745 = sin(r173744);
        double r173746 = r173745 / r173744;
        double r173747 = r173743 * r173746;
        return r173747;
}
↓
double f(double x, double y) {
        double r173748 = y;
        double r173749 = sin(r173748);
        double r173750 = r173749 / r173748;
        double r173751 = x;
        double r173752 = r173750 * r173751;
        return r173752;
}

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 *-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 2020042 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))