Average Error: 0.1 → 0.1
Time: 31.4s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r357787 = x;
        double r357788 = cosh(r357787);
        double r357789 = y;
        double r357790 = sin(r357789);
        double r357791 = r357790 / r357789;
        double r357792 = r357788 * r357791;
        return r357792;
}
↓
double f(double x, double y) {
        double r357793 = x;
        double r357794 = cosh(r357793);
        double r357795 = y;
        double r357796 = sin(r357795);
        double r357797 = r357796 / r357795;
        double r357798 = r357794 * r357797;
        return r357798;
}

Error

Bits error versus x

Bits error versus y

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Results

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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. Final simplification0.1

    \[\leadsto \cosh x \cdot \frac{\sin y}{y}\]

Reproduce

herbie shell --seed 2019326 +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)))