Average Error: 0.1 → 0.1
Time: 3.1s
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 r129442 = x;
        double r129443 = y;
        double r129444 = sin(r129443);
        double r129445 = r129444 / r129443;
        double r129446 = r129442 * r129445;
        return r129446;
}
↓
double f(double x, double y) {
        double r129447 = x;
        double r129448 = y;
        double r129449 = sin(r129448);
        double r129450 = r129448 / r129449;
        double r129451 = r129447 / r129450;
        return r129451;
}

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. Using strategy rm

  3. Applied associate-*r/7.3

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

  5. Applied associate-/l*0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020064 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))