Average Error: 0.1 → 0.1
Time: 19.0s
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 r350824 = x;
        double r350825 = cosh(r350824);
        double r350826 = y;
        double r350827 = sin(r350826);
        double r350828 = r350827 / r350826;
        double r350829 = r350825 * r350828;
        return r350829;
}
↓
double f(double x, double y) {
        double r350830 = x;
        double r350831 = cosh(r350830);
        double r350832 = y;
        double r350833 = sin(r350832);
        double r350834 = r350833 / r350832;
        double r350835 = r350831 * r350834;
        return r350835;
}

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 2019198 +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)))