Average Error: 0.1 → 0.1
Time: 7.9s
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 r133611 = x;
        double r133612 = y;
        double r133613 = sin(r133612);
        double r133614 = r133613 / r133612;
        double r133615 = r133611 * r133614;
        return r133615;
}
↓
double f(double x, double y) {
        double r133616 = x;
        double r133617 = y;
        double r133618 = sin(r133617);
        double r133619 = r133617 / r133618;
        double r133620 = r133616 / r133619;
        return r133620;
}

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. Using strategy rm

  5. Applied *-un-lft-identity0.2

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

  6. Applied associate-*l*0.2

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

  7. Simplified7.2

    \[\leadsto 1 \cdot \color{blue}{\frac{x \cdot \sin y}{y}}\]
  8. Using strategy rm

  9. Applied associate-/l*0.1

    \[\leadsto 1 \cdot \color{blue}{\frac{x}{\frac{y}{\sin y}}}\]

  10. Final simplification0.1

    \[\leadsto \frac{x}{\frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))