Average Error: 0.1 → 0.2
Time: 13.0s
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 r7395571 = x;
        double r7395572 = y;
        double r7395573 = sin(r7395572);
        double r7395574 = r7395573 / r7395572;
        double r7395575 = r7395571 * r7395574;
        return r7395575;
}
↓
double f(double x, double y) {
        double r7395576 = 1.0;
        double r7395577 = y;
        double r7395578 = r7395576 / r7395577;
        double r7395579 = sin(r7395577);
        double r7395580 = r7395578 * r7395579;
        double r7395581 = x;
        double r7395582 = r7395580 * r7395581;
        return r7395582;
}

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 div-inv0.2

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

  4. Final simplification0.2

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

Reproduce

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