Average Error: 0.1 → 0.1
Time: 8.4s
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 r133229 = x;
        double r133230 = y;
        double r133231 = sin(r133230);
        double r133232 = r133231 / r133230;
        double r133233 = r133229 * r133232;
        return r133233;
}
↓
double f(double x, double y) {
        double r133234 = x;
        double r133235 = y;
        double r133236 = sin(r133235);
        double r133237 = r133235 / r133236;
        double r133238 = r133234 / r133237;
        return r133238;
}

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 pow10.1

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

  4. Applied pow10.1

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

  5. Applied pow-prod-down0.1

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

  6. Simplified7.2

    \[\leadsto {\color{blue}{\left(\frac{x \cdot \sin y}{y}\right)}}^{1}\]
  7. Using strategy rm

  8. Applied associate-/l*0.1

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

  9. Final simplification0.1

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

Reproduce

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