Average Error: 0.1 → 0.1
Time: 10.1s
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 r103852 = x;
        double r103853 = y;
        double r103854 = sin(r103853);
        double r103855 = r103854 / r103853;
        double r103856 = r103852 * r103855;
        return r103856;
}
↓
double f(double x, double y) {
        double r103857 = y;
        double r103858 = sin(r103857);
        double r103859 = r103858 / r103857;
        double r103860 = x;
        double r103861 = r103859 * r103860;
        return r103861;
}

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 *-commutative0.1

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

  5. Applied clear-num0.2

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

  7. Applied *-un-lft-identity0.2

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

  8. Applied associate-*r*0.2

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019294 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))