Average Error: 13.7 → 0.1
Time: 32.6s
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 r24180244 = x;
        double r24180245 = sin(r24180244);
        double r24180246 = y;
        double r24180247 = sinh(r24180246);
        double r24180248 = r24180245 * r24180247;
        double r24180249 = r24180248 / r24180244;
        return r24180249;
}
↓
double f(double x, double y) {
        double r24180250 = y;
        double r24180251 = sinh(r24180250);
        double r24180252 = x;
        double r24180253 = sin(r24180252);
        double r24180254 = r24180253 / r24180252;
        double r24180255 = r24180251 * r24180254;
        return r24180255;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.7
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.7

    \[\frac{\sin x \cdot \sinh y}{x}\]
  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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(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))