Average Error: 0.1 → 0.1
Time: 20.7s
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 r118816 = x;
        double r118817 = y;
        double r118818 = sin(r118817);
        double r118819 = r118818 / r118817;
        double r118820 = r118816 * r118819;
        return r118820;
}
↓
double f(double x, double y) {
        double r118821 = y;
        double r118822 = sin(r118821);
        double r118823 = r118822 / r118821;
        double r118824 = x;
        double r118825 = r118823 * r118824;
        return r118825;
}

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