Average Error: 0.1 → 0.2
Time: 3.4s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{1}{\frac{y}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{1}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r116631 = x;
        double r116632 = y;
        double r116633 = sin(r116632);
        double r116634 = r116633 / r116632;
        double r116635 = r116631 * r116634;
        return r116635;
}
↓
double f(double x, double y) {
        double r116636 = x;
        double r116637 = 1.0;
        double r116638 = y;
        double r116639 = sin(r116638);
        double r116640 = r116638 / r116639;
        double r116641 = r116637 / r116640;
        double r116642 = r116636 * r116641;
        return r116642;
}

Error

Bits error versus x

Bits error versus y

Try it out

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))