Average Error: 0.1 → 0.1
Time: 4.1s
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 r130720 = x;
        double r130721 = y;
        double r130722 = sin(r130721);
        double r130723 = r130722 / r130721;
        double r130724 = r130720 * r130723;
        return r130724;
}
↓
double f(double x, double y) {
        double r130725 = x;
        double r130726 = y;
        double r130727 = sin(r130726);
        double r130728 = r130726 / r130727;
        double r130729 = r130725 / r130728;
        return r130729;
}

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 *-un-lft-identity0.1

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

  4. Applied associate-*l*0.1

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

  5. Simplified7.2

    \[\leadsto 1 \cdot \color{blue}{\frac{x \cdot \sin y}{y}}\]
  6. Using strategy rm

  7. Applied associate-/l*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))