Average Error: 0.1 → 0.3
Time: 15.4s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\left(\frac{1}{y} \cdot \sin y\right) \cdot x\]
x \cdot \frac{\sin y}{y}
↓
\left(\frac{1}{y} \cdot \sin y\right) \cdot x
double f(double x, double y) {
        double r117666 = x;
        double r117667 = y;
        double r117668 = sin(r117667);
        double r117669 = r117668 / r117667;
        double r117670 = r117666 * r117669;
        return r117670;
}
↓
double f(double x, double y) {
        double r117671 = 1.0;
        double r117672 = y;
        double r117673 = r117671 / r117672;
        double r117674 = sin(r117672);
        double r117675 = r117673 * r117674;
        double r117676 = x;
        double r117677 = r117675 * r117676;
        return r117677;
}

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. Simplified0.1

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

  4. Applied div-inv0.3

    \[\leadsto \color{blue}{\left(\sin y \cdot \frac{1}{y}\right)} \cdot x\]

  5. Final simplification0.3

    \[\leadsto \left(\frac{1}{y} \cdot \sin y\right) \cdot x\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))