Average Error: 0.1 → 0.1
Time: 17.2s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\cosh x \cdot \sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\cosh x \cdot \sin y}{y}
double f(double x, double y) {
        double r404653 = x;
        double r404654 = cosh(r404653);
        double r404655 = y;
        double r404656 = sin(r404655);
        double r404657 = r404656 / r404655;
        double r404658 = r404654 * r404657;
        return r404658;
}
↓
double f(double x, double y) {
        double r404659 = x;
        double r404660 = cosh(r404659);
        double r404661 = y;
        double r404662 = sin(r404661);
        double r404663 = r404660 * r404662;
        double r404664 = r404663 / r404661;
        return r404664;
}

Error

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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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"

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

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