Average Error: 0.1 → 0.1
Time: 8.9s
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 r99975 = x;
        double r99976 = y;
        double r99977 = sin(r99976);
        double r99978 = r99977 / r99976;
        double r99979 = r99975 * r99978;
        return r99979;
}
↓
double f(double x, double y) {
        double r99980 = x;
        double r99981 = y;
        double r99982 = sin(r99981);
        double r99983 = r99981 / r99982;
        double r99984 = r99980 / r99983;
        return r99984;
}

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 pow10.2

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

  6. Applied pow10.2

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

  7. Applied pow-prod-down0.2

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))