Average Error: 0.1 → 0.2
Time: 12.3s
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 r5577842 = x;
        double r5577843 = y;
        double r5577844 = sin(r5577843);
        double r5577845 = r5577844 / r5577843;
        double r5577846 = r5577842 * r5577845;
        return r5577846;
}
↓
double f(double x, double y) {
        double r5577847 = x;
        double r5577848 = y;
        double r5577849 = sin(r5577848);
        double r5577850 = r5577848 / r5577849;
        double r5577851 = r5577847 / r5577850;
        return r5577851;
}

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. 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 2019164 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))