Average Error: 0.1 → 0.1
Time: 10.9s
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 r88783 = x;
        double r88784 = y;
        double r88785 = sin(r88784);
        double r88786 = r88785 / r88784;
        double r88787 = r88783 * r88786;
        return r88787;
}
↓
double f(double x, double y) {
        double r88788 = x;
        double r88789 = y;
        double r88790 = sin(r88789);
        double r88791 = r88789 / r88790;
        double r88792 = r88788 / r88791;
        return r88792;
}

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. Simplified0.1

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

  4. Applied div-inv0.2

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

  6. Applied un-div-inv0.1

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

  7. Applied associate-*l/6.9

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

  8. Taylor expanded around inf 6.9

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  (* x (/ (sin y) y)))