Average Error: 13.9 → 0.1
Time: 18.5s
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 r427507 = x;
        double r427508 = sin(r427507);
        double r427509 = y;
        double r427510 = sinh(r427509);
        double r427511 = r427508 * r427510;
        double r427512 = r427511 / r427507;
        return r427512;
}
↓
double f(double x, double y) {
        double r427513 = y;
        double r427514 = sinh(r427513);
        double r427515 = x;
        double r427516 = sin(r427515);
        double r427517 = r427516 / r427515;
        double r427518 = r427514 * r427517;
        return r427518;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.9
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.9

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

  2. Simplified0.8

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

  4. Applied div-inv0.9

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

  5. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{\sin x}{x}}{\frac{1}{\sinh y}}}\]
  6. Using strategy rm

  7. Applied div-inv0.2

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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))