Average Error: 0.2 → 0.2
Time: 3.9s
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 r689776 = x;
        double r689777 = cosh(r689776);
        double r689778 = y;
        double r689779 = sin(r689778);
        double r689780 = r689779 / r689778;
        double r689781 = r689777 * r689780;
        return r689781;
}
↓
double f(double x, double y) {
        double r689782 = x;
        double r689783 = cosh(r689782);
        double r689784 = y;
        double r689785 = sin(r689784);
        double r689786 = r689785 / r689784;
        double r689787 = r689783 * r689786;
        return r689787;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2020025 +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)))