Average Error: 14.5 → 0.2
Time: 29.2s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\sinh y}{x}
double f(double x, double y) {
        double r351810 = x;
        double r351811 = sin(r351810);
        double r351812 = y;
        double r351813 = sinh(r351812);
        double r351814 = r351811 * r351813;
        double r351815 = r351814 / r351810;
        return r351815;
}
↓
double f(double x, double y) {
        double r351816 = x;
        double r351817 = sin(r351816);
        double r351818 = y;
        double r351819 = sinh(r351818);
        double r351820 = r351819 / r351816;
        double r351821 = r351817 * r351820;
        return r351821;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.5
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.5

    \[\frac{\sin x \cdot \sinh y}{x}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity14.5

    \[\leadsto \frac{\sin x \cdot \sinh y}{\color{blue}{1 \cdot x}}\]

  4. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{\sin x}{1} \cdot \frac{\sinh y}{x}}\]

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

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

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