Average Error: 13.8 → 0.1
Time: 4.2s
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 r589433 = x;
        double r589434 = sin(r589433);
        double r589435 = y;
        double r589436 = sinh(r589435);
        double r589437 = r589434 * r589436;
        double r589438 = r589437 / r589433;
        return r589438;
}
↓
double f(double x, double y) {
        double r589439 = x;
        double r589440 = sin(r589439);
        double r589441 = r589440 / r589439;
        double r589442 = y;
        double r589443 = sinh(r589442);
        double r589444 = r589441 * r589443;
        return r589444;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original13.8
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.8

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

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

Reproduce

herbie shell --seed 2020035 +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))