Average Error: 14.6 → 0.1
Time: 10.5s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{x} \cdot \sinh y\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{x} \cdot \sinh y
double f(double x, double y) {
        double r630382 = x;
        double r630383 = sin(r630382);
        double r630384 = y;
        double r630385 = sinh(r630384);
        double r630386 = r630383 * r630385;
        double r630387 = r630386 / r630382;
        return r630387;
}
↓
double f(double x, double y) {
        double r630388 = x;
        double r630389 = sin(r630388);
        double r630390 = r630389 / r630388;
        double r630391 = y;
        double r630392 = sinh(r630391);
        double r630393 = r630390 * r630392;
        return r630393;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.6
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.6

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

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

Reproduce

herbie shell --seed 2020047 
(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))