Average Error: 0.1 → 0.1
Time: 5.6s
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 r456034 = x;
        double r456035 = cosh(r456034);
        double r456036 = y;
        double r456037 = sin(r456036);
        double r456038 = r456037 / r456036;
        double r456039 = r456035 * r456038;
        return r456039;
}
↓
double f(double x, double y) {
        double r456040 = x;
        double r456041 = cosh(r456040);
        double r456042 = y;
        double r456043 = sin(r456042);
        double r456044 = r456043 / r456042;
        double r456045 = expm1(r456044);
        double r456046 = log1p(r456045);
        double r456047 = r456041 * r456046;
        return r456047;
}

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 2019354 +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)))