Average Error: 14.6 → 0.1
Time: 18.3s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sinh y \cdot \frac{\sin x}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{\sin x}{x}
double f(double x, double y) {
        double r396990 = x;
        double r396991 = sin(r396990);
        double r396992 = y;
        double r396993 = sinh(r396992);
        double r396994 = r396991 * r396993;
        double r396995 = r396994 / r396990;
        return r396995;
}
↓
double f(double x, double y) {
        double r396996 = y;
        double r396997 = sinh(r396996);
        double r396998 = x;
        double r396999 = sin(r396998);
        double r397000 = r396999 / r396998;
        double r397001 = r396997 * r397000;
        return r397001;
}

Error

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Bits error versus y

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Results

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Target

Original14.6
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.6

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

  2. Simplified0.7

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  3. Using strategy rm

  4. Applied associate-/r/0.1

    \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y}\]

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))