Average Error: 0.1 → 0.1
Time: 28.0s
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 r445755 = x;
        double r445756 = cosh(r445755);
        double r445757 = y;
        double r445758 = sin(r445757);
        double r445759 = r445758 / r445757;
        double r445760 = r445756 * r445759;
        return r445760;
}
↓
double f(double x, double y) {
        double r445761 = x;
        double r445762 = cosh(r445761);
        double r445763 = y;
        double r445764 = sin(r445763);
        double r445765 = r445764 / r445763;
        double r445766 = expm1(r445765);
        double r445767 = log1p(r445766);
        double r445768 = r445762 * r445767;
        return r445768;
}

Error

Bits error versus x

Bits error versus y

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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)))