Average Error: 0.1 → 0.1
Time: 3.5s
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 r107413 = x;
        double r107414 = y;
        double r107415 = sin(r107414);
        double r107416 = r107415 / r107414;
        double r107417 = r107413 * r107416;
        return r107417;
}
↓
double f(double x, double y) {
        double r107418 = x;
        double r107419 = y;
        double r107420 = sin(r107419);
        double r107421 = r107419 / r107420;
        double r107422 = r107418 / r107421;
        return r107422;
}

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/7.0

    \[\leadsto \color{blue}{\frac{x \cdot \sin y}{y}}\]
  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 2020027 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))