Average Error: 0.1 → 0.2
Time: 3.9s
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 r137533 = x;
        double r137534 = y;
        double r137535 = sin(r137534);
        double r137536 = r137535 / r137534;
        double r137537 = r137533 * r137536;
        return r137537;
}
↓
double f(double x, double y) {
        double r137538 = x;
        double r137539 = y;
        double r137540 = sin(r137539);
        double r137541 = r137539 / r137540;
        double r137542 = r137538 / r137541;
        return r137542;
}

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/7.4

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

  5. Applied associate-/l*0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))