Average Error: 0.1 → 0.2
Time: 3.4s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{1}{\frac{y}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{1}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r121095 = x;
        double r121096 = y;
        double r121097 = sin(r121096);
        double r121098 = r121097 / r121096;
        double r121099 = r121095 * r121098;
        return r121099;
}
↓
double f(double x, double y) {
        double r121100 = x;
        double r121101 = 1.0;
        double r121102 = y;
        double r121103 = sin(r121102);
        double r121104 = r121102 / r121103;
        double r121105 = r121101 / r121104;
        double r121106 = r121100 * r121105;
        return r121106;
}

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))