Average Error: 14.4 → 0.2
Time: 10.8s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}
double f(double x, double y) {
        double r409910 = x;
        double r409911 = sin(r409910);
        double r409912 = y;
        double r409913 = sinh(r409912);
        double r409914 = r409911 * r409913;
        double r409915 = r409914 / r409910;
        return r409915;
}
↓
double f(double x, double y) {
        double r409916 = x;
        double r409917 = sin(r409916);
        double r409918 = r409917 / r409916;
        double r409919 = 1.0;
        double r409920 = y;
        double r409921 = sinh(r409920);
        double r409922 = r409919 / r409921;
        double r409923 = r409918 / r409922;
        return r409923;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.4
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.4

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

  3. Applied associate-/l*0.7

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

  5. Applied div-inv0.8

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

  6. Applied associate-/r*0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(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))