Average Error: 14.4 → 0.2
Time: 12.3s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\sinh y}{x}
double f(double x, double y) {
        double r356593 = x;
        double r356594 = sin(r356593);
        double r356595 = y;
        double r356596 = sinh(r356595);
        double r356597 = r356594 * r356596;
        double r356598 = r356597 / r356593;
        return r356598;
}
↓
double f(double x, double y) {
        double r356599 = x;
        double r356600 = sin(r356599);
        double r356601 = y;
        double r356602 = sinh(r356601);
        double r356603 = r356602 / r356599;
        double r356604 = r356600 * r356603;
        return r356604;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.4
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.4

    \[\frac{\sin x \cdot \sinh y}{x}\]
  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 clear-num0.9

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

  7. Applied div-inv1.0

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

  8. Applied associate-/r*0.9

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

  9. Simplified0.4

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019303 
(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))