Average Error: 0.1 → 0.1
Time: 5.9s
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 r517952 = x;
        double r517953 = cosh(r517952);
        double r517954 = y;
        double r517955 = sin(r517954);
        double r517956 = r517955 / r517954;
        double r517957 = r517953 * r517956;
        return r517957;
}
↓
double f(double x, double y) {
        double r517958 = x;
        double r517959 = cosh(r517958);
        double r517960 = y;
        double r517961 = sin(r517960);
        double r517962 = r517961 / r517960;
        double r517963 = r517959 * r517962;
        return r517963;
}

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 2020001 +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)))