Average Error: 13.4 → 0.1
Time: 4.3s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{1}{\frac{x}{\sin x}} \cdot \sinh y\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{1}{\frac{x}{\sin x}} \cdot \sinh y
double f(double x, double y) {
        double r454788 = x;
        double r454789 = sin(r454788);
        double r454790 = y;
        double r454791 = sinh(r454790);
        double r454792 = r454789 * r454791;
        double r454793 = r454792 / r454788;
        return r454793;
}
↓
double f(double x, double y) {
        double r454794 = 1.0;
        double r454795 = x;
        double r454796 = sin(r454795);
        double r454797 = r454795 / r454796;
        double r454798 = r454794 / r454797;
        double r454799 = y;
        double r454800 = sinh(r454799);
        double r454801 = r454798 * r454800;
        return r454801;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.4
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.4

    \[\frac{\sin x \cdot \sinh y}{x}\]
  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 associate-/r/0.1

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

  7. Applied clear-num0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 +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))