Average Error: 0.1 → 0.1
Time: 6.3s
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 r618390 = x;
        double r618391 = cosh(r618390);
        double r618392 = y;
        double r618393 = sin(r618392);
        double r618394 = r618393 / r618392;
        double r618395 = r618391 * r618394;
        return r618395;
}
↓
double f(double x, double y) {
        double r618396 = x;
        double r618397 = cosh(r618396);
        double r618398 = y;
        double r618399 = sin(r618398);
        double r618400 = r618399 / r618398;
        double r618401 = r618397 * r618400;
        return r618401;
}

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 2019362 +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)))