Average Error: 0.1 → 0.1
Time: 19.6s
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 r104745 = x;
        double r104746 = y;
        double r104747 = sin(r104746);
        double r104748 = r104747 / r104746;
        double r104749 = r104745 * r104748;
        return r104749;
}
↓
double f(double x, double y) {
        double r104750 = y;
        double r104751 = sin(r104750);
        double r104752 = r104751 / r104750;
        double r104753 = x;
        double r104754 = r104752 * r104753;
        return r104754;
}

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 2019323 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))