Average Error: 0.1 → 0.2
Time: 3.5s
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 r117980 = x;
        double r117981 = y;
        double r117982 = sin(r117981);
        double r117983 = r117982 / r117981;
        double r117984 = r117980 * r117983;
        return r117984;
}
↓
double f(double x, double y) {
        double r117985 = x;
        double r117986 = y;
        double r117987 = sin(r117986);
        double r117988 = r117986 / r117987;
        double r117989 = r117985 / r117988;
        return r117989;
}

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 clear-num0.2

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

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

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

  6. Applied associate-*l*0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))