Average Error: 0.1 → 0.1
Time: 12.6s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{\sin y}{y}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r80435 = x;
        double r80436 = y;
        double r80437 = sin(r80436);
        double r80438 = r80437 / r80436;
        double r80439 = r80435 * r80438;
        return r80439;
}
↓
double f(double x, double y) {
        double r80440 = x;
        double r80441 = y;
        double r80442 = sin(r80441);
        double r80443 = r80442 / r80441;
        double r80444 = r80440 * r80443;
        return r80444;
}

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-lft-identity0.2

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

  6. Applied associate-*l*0.2

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

  7. Simplified0.2

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

  9. Applied div-inv0.2

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))