Average Error: 0.1 → 0.5
Time: 14.4s
Precision: 64
\[x \gt 0\]
\[\frac{\sin x}{x} \cdot y\]
\[\frac{\frac{\sin x}{\sqrt{x}}}{\sqrt{x}} \cdot y\]
\frac{\sin x}{x} \cdot y
\frac{\frac{\sin x}{\sqrt{x}}}{\sqrt{x}} \cdot y
double f(double x, double y) {
        double r37244452 = x;
        double r37244453 = sin(r37244452);
        double r37244454 = r37244453 / r37244452;
        double r37244455 = y;
        double r37244456 = r37244454 * r37244455;
        return r37244456;
}

double f(double x, double y) {
        double r37244457 = x;
        double r37244458 = sin(r37244457);
        double r37244459 = sqrt(r37244457);
        double r37244460 = r37244458 / r37244459;
        double r37244461 = r37244460 / r37244459;
        double r37244462 = y;
        double r37244463 = r37244461 * r37244462;
        return r37244463;
}

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

    \[\frac{\sin x}{x} \cdot y\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.5

    \[\leadsto \frac{\sin x}{\color{blue}{\sqrt{x} \cdot \sqrt{x}}} \cdot y\]
  4. Applied associate-/r*0.5

    \[\leadsto \color{blue}{\frac{\frac{\sin x}{\sqrt{x}}}{\sqrt{x}}} \cdot y\]
  5. Final simplification0.5

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

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "(sin(x)/x)*y"
  :pre (> x 0)
  (* (/ (sin x) x) y))