Average Error: 14.0 → 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 r407931 = x;
        double r407932 = sin(r407931);
        double r407933 = y;
        double r407934 = sinh(r407933);
        double r407935 = r407932 * r407934;
        double r407936 = r407935 / r407931;
        return r407936;
}
↓
double f(double x, double y) {
        double r407937 = y;
        double r407938 = sinh(r407937);
        double r407939 = x;
        double r407940 = sin(r407939);
        double r407941 = r407940 / r407939;
        double r407942 = r407938 * r407941;
        return r407942;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.0
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  2. Simplified0.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  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 2019196 
(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))