Average Error: 14.0 → 0.1
Time: 15.9s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sinh y \cdot \frac{1}{\frac{x}{\sin x}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{1}{\frac{x}{\sin x}}
double f(double x, double y) {
        double r19648244 = x;
        double r19648245 = sin(r19648244);
        double r19648246 = y;
        double r19648247 = sinh(r19648246);
        double r19648248 = r19648245 * r19648247;
        double r19648249 = r19648248 / r19648244;
        return r19648249;
}
↓
double f(double x, double y) {
        double r19648250 = y;
        double r19648251 = sinh(r19648250);
        double r19648252 = 1.0;
        double r19648253 = x;
        double r19648254 = sin(r19648253);
        double r19648255 = r19648253 / r19648254;
        double r19648256 = r19648252 / r19648255;
        double r19648257 = r19648251 * r19648256;
        return r19648257;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.0
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  3. Applied associate-/l*0.8

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

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

Reproduce

herbie shell --seed 2019179 +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))