Average Error: 0.1 → 0.2
Time: 3.5s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \left(\sin y \cdot \frac{1}{y}\right)\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \left(\sin y \cdot \frac{1}{y}\right)
double f(double x, double y) {
        double r166964 = x;
        double r166965 = y;
        double r166966 = sin(r166965);
        double r166967 = r166966 / r166965;
        double r166968 = r166964 * r166967;
        return r166968;
}
↓
double f(double x, double y) {
        double r166969 = x;
        double r166970 = y;
        double r166971 = sin(r166970);
        double r166972 = 1.0;
        double r166973 = r166972 / r166970;
        double r166974 = r166971 * r166973;
        double r166975 = r166969 * r166974;
        return r166975;
}

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 div-inv0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020039 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))