Average Error: 0.1 → 0.2
Time: 3.6s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\frac{1}{\frac{y}{\sin y}} \cdot x\]
x \cdot \frac{\sin y}{y}
↓
\frac{1}{\frac{y}{\sin y}} \cdot x
double f(double x, double y) {
        double r138691 = x;
        double r138692 = y;
        double r138693 = sin(r138692);
        double r138694 = r138693 / r138692;
        double r138695 = r138691 * r138694;
        return r138695;
}
↓
double f(double x, double y) {
        double r138696 = 1.0;
        double r138697 = y;
        double r138698 = sin(r138697);
        double r138699 = r138697 / r138698;
        double r138700 = r138696 / r138699;
        double r138701 = x;
        double r138702 = r138700 * r138701;
        return r138702;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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 *-commutative0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{\sin y}} \cdot x}\]

  6. Final simplification0.2

    \[\leadsto \frac{1}{\frac{y}{\sin y}} \cdot x\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))