Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \frac{1}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\sinh y}\right)\right)}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \frac{1}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\sinh y}\right)\right)}
double f(double x, double y) {
        double r167544 = x;
        double r167545 = cos(r167544);
        double r167546 = y;
        double r167547 = sinh(r167546);
        double r167548 = r167547 / r167546;
        double r167549 = r167545 * r167548;
        return r167549;
}
↓
double f(double x, double y) {
        double r167550 = x;
        double r167551 = cos(r167550);
        double r167552 = 1.0;
        double r167553 = y;
        double r167554 = sinh(r167553);
        double r167555 = r167553 / r167554;
        double r167556 = log1p(r167555);
        double r167557 = expm1(r167556);
        double r167558 = r167552 / r167557;
        double r167559 = r167551 * r167558;
        return r167559;
}

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 0.0

    \[\cos x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto \cos x \cdot \color{blue}{\frac{1}{\frac{y}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied expm1-log1p-u0.0

    \[\leadsto \cos x \cdot \frac{1}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\sinh y}\right)\right)}}\]

  6. Final simplification0.0

    \[\leadsto \cos x \cdot \frac{1}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{\sinh y}\right)\right)}\]

Reproduce

herbie shell --seed 2019346 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))