Average Error: 13.9 → 0.1
Time: 19.4s
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 r428695 = x;
        double r428696 = sin(r428695);
        double r428697 = y;
        double r428698 = sinh(r428697);
        double r428699 = r428696 * r428698;
        double r428700 = r428699 / r428695;
        return r428700;
}
↓
double f(double x, double y) {
        double r428701 = y;
        double r428702 = sinh(r428701);
        double r428703 = x;
        double r428704 = sin(r428703);
        double r428705 = r428704 / r428703;
        double r428706 = r428702 * r428705;
        return r428706;
}

Error

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Bits error versus y

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Results

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Target

Original13.9
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.9

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(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))