Average Error: 0.1 → 0.1
Time: 20.6s
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 r128338 = x;
        double r128339 = y;
        double r128340 = sin(r128339);
        double r128341 = r128340 / r128339;
        double r128342 = r128338 * r128341;
        return r128342;
}
↓
double f(double x, double y) {
        double r128343 = y;
        double r128344 = sin(r128343);
        double r128345 = r128344 / r128343;
        double r128346 = x;
        double r128347 = r128345 * r128346;
        return r128347;
}

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)))