Average Error: 0.1 → 0.2
Time: 15.9s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\frac{x}{\frac{y}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
\frac{x}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r7488645 = x;
        double r7488646 = y;
        double r7488647 = sin(r7488646);
        double r7488648 = r7488647 / r7488646;
        double r7488649 = r7488645 * r7488648;
        return r7488649;
}
↓
double f(double x, double y) {
        double r7488650 = x;
        double r7488651 = y;
        double r7488652 = sin(r7488651);
        double r7488653 = r7488651 / r7488652;
        double r7488654 = r7488650 / r7488653;
        return r7488654;
}

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 clear-num0.2

    \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\]
  4. Using strategy rm

  5. Applied un-div-inv0.2

    \[\leadsto \color{blue}{\frac{x}{\frac{y}{\sin y}}}\]

  6. Final simplification0.2

    \[\leadsto \frac{x}{\frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))