Average Error: 0.1 → 0.1
Time: 9.4s
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 r107502 = x;
        double r107503 = y;
        double r107504 = sin(r107503);
        double r107505 = r107504 / r107503;
        double r107506 = r107502 * r107505;
        return r107506;
}
↓
double f(double x, double y) {
        double r107507 = y;
        double r107508 = sin(r107507);
        double r107509 = r107508 / r107507;
        double r107510 = x;
        double r107511 = r107509 * r107510;
        return r107511;
}

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 2019196 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))