Average Error: 0.1 → 0.1
Time: 12.6s
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 r107215 = x;
        double r107216 = y;
        double r107217 = sin(r107216);
        double r107218 = r107217 / r107216;
        double r107219 = r107215 * r107218;
        return r107219;
}
↓
double f(double x, double y) {
        double r107220 = x;
        double r107221 = y;
        double r107222 = sin(r107221);
        double r107223 = r107221 / r107222;
        double r107224 = r107220 / r107223;
        return r107224;
}

Error

Bits error versus x

Bits error versus y

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Results

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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 div-inv0.2

    \[\leadsto \color{blue}{\left(\sin y \cdot \frac{1}{y}\right)} \cdot x\]

  5. Taylor expanded around inf 6.9

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))