Average Error: 0.1 → 0.1
Time: 7.9s
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 r688549 = x;
        double r688550 = cosh(r688549);
        double r688551 = y;
        double r688552 = sin(r688551);
        double r688553 = r688552 / r688551;
        double r688554 = r688550 * r688553;
        return r688554;
}
↓
double f(double x, double y) {
        double r688555 = x;
        double r688556 = cosh(r688555);
        double r688557 = y;
        double r688558 = sin(r688557);
        double r688559 = r688558 / r688557;
        double r688560 = r688556 * r688559;
        return r688560;
}

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 2020060 +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)))