Average Error: 0.1 → 0.1
Time: 3.9s
Precision: 64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{\sin y}{y}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r105786 = x;
        double r105787 = y;
        double r105788 = sin(r105787);
        double r105789 = r105788 / r105787;
        double r105790 = r105786 * r105789;
        return r105790;
}
↓
double f(double x, double y) {
        double r105791 = x;
        double r105792 = y;
        double r105793 = sin(r105792);
        double r105794 = r105793 / r105792;
        double r105795 = r105791 * r105794;
        return r105795;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))