Average Error: 0.1 → 0.2
Time: 11.7s
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 r99433 = x;
        double r99434 = y;
        double r99435 = sin(r99434);
        double r99436 = r99435 / r99434;
        double r99437 = r99433 * r99436;
        return r99437;
}
↓
double f(double x, double y) {
        double r99438 = x;
        double r99439 = y;
        double r99440 = sin(r99439);
        double r99441 = r99439 / r99440;
        double r99442 = r99438 / r99441;
        return r99442;
}

Error

Bits error versus x

Bits error versus y

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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 clear-num0.2

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

  6. Applied associate-*l/0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))