Average Error: 0.1 → 0.1
Time: 11.1s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\sin y}{y} \cdot x\]
x \cdot \frac{\sin y}{y}
↓
\frac{\sin y}{y} \cdot x
double f(double x, double y) {
        double r5225781 = x;
        double r5225782 = y;
        double r5225783 = sin(r5225782);
        double r5225784 = r5225783 / r5225782;
        double r5225785 = r5225781 * r5225784;
        return r5225785;
}
↓
double f(double x, double y) {
        double r5225786 = y;
        double r5225787 = sin(r5225786);
        double r5225788 = r5225787 / r5225786;
        double r5225789 = x;
        double r5225790 = r5225788 * r5225789;
        return r5225790;
}

Error

Bits error versus x

Bits error versus y

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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. Taylor expanded around inf 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))