Average Error: 0.0 → 0.3
Time: 23.2s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cos x \cdot \sinh y}{y}\right)\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\cos x \cdot \sinh y}{y}\right)\right)
double f(double x, double y) {
        double r129438 = x;
        double r129439 = cos(r129438);
        double r129440 = y;
        double r129441 = sinh(r129440);
        double r129442 = r129441 / r129440;
        double r129443 = r129439 * r129442;
        return r129443;
}
↓
double f(double x, double y) {
        double r129444 = x;
        double r129445 = cos(r129444);
        double r129446 = y;
        double r129447 = sinh(r129446);
        double r129448 = r129445 * r129447;
        double r129449 = r129448 / r129446;
        double r129450 = log1p(r129449);
        double r129451 = expm1(r129450);
        return r129451;
}

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 expm1-log1p-u0.3

    \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\cos x \cdot \frac{\sinh y}{y}\right)\right)}\]
  4. Using strategy rm

  5. Applied associate-*r/0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))