Average Error: 0.1 → 0.2
Time: 13.6s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\left(\sin y \cdot \frac{1}{y}\right) \cdot x\]
x \cdot \frac{\sin y}{y}
↓
\left(\sin y \cdot \frac{1}{y}\right) \cdot x
double f(double x, double y) {
        double r11452556 = x;
        double r11452557 = y;
        double r11452558 = sin(r11452557);
        double r11452559 = r11452558 / r11452557;
        double r11452560 = r11452556 * r11452559;
        return r11452560;
}
↓
double f(double x, double y) {
        double r11452561 = y;
        double r11452562 = sin(r11452561);
        double r11452563 = 1.0;
        double r11452564 = r11452563 / r11452561;
        double r11452565 = r11452562 * r11452564;
        double r11452566 = x;
        double r11452567 = r11452565 * r11452566;
        return r11452567;
}

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 *-commutative0.1

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

  5. Applied div-inv0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))