Average Error: 0.1 → 0.1
Time: 27.1s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin y}{y}\right)\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{\sin y}{y}\right)\right)
double f(double x, double y) {
        double r361198 = x;
        double r361199 = cosh(r361198);
        double r361200 = y;
        double r361201 = sin(r361200);
        double r361202 = r361201 / r361200;
        double r361203 = r361199 * r361202;
        return r361203;
}
↓
double f(double x, double y) {
        double r361204 = x;
        double r361205 = cosh(r361204);
        double r361206 = y;
        double r361207 = sin(r361206);
        double r361208 = r361207 / r361206;
        double r361209 = expm1(r361208);
        double r361210 = log1p(r361209);
        double r361211 = r361205 * r361210;
        return r361211;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.1
Herbie0.1
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied log1p-expm1-u0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))