Average Error: 13.9 → 0.1
Time: 17.4s
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 r366861 = x;
        double r366862 = sin(r366861);
        double r366863 = y;
        double r366864 = sinh(r366863);
        double r366865 = r366862 * r366864;
        double r366866 = r366865 / r366861;
        return r366866;
}
↓
double f(double x, double y) {
        double r366867 = y;
        double r366868 = sinh(r366867);
        double r366869 = x;
        double r366870 = sin(r366869);
        double r366871 = r366870 / r366869;
        double r366872 = r366868 * r366871;
        return r366872;
}

Error

Bits error versus x

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 2019174 +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))