Average Error: 0.1 → 0.2
Time: 11.5s
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 r167749 = x;
        double r167750 = y;
        double r167751 = sin(r167750);
        double r167752 = r167751 / r167750;
        double r167753 = r167749 * r167752;
        return r167753;
}
↓
double f(double x, double y) {
        double r167754 = x;
        double r167755 = 1.0;
        double r167756 = y;
        double r167757 = sin(r167756);
        double r167758 = r167756 / r167757;
        double r167759 = r167755 / r167758;
        double r167760 = r167754 * r167759;
        return r167760;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))