Average Error: 14.5 → 0.1
Time: 35.5s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sinh y}{\frac{x}{\sin x}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sinh y}{\frac{x}{\sin x}}
double f(double x, double y) {
        double r308549 = x;
        double r308550 = sin(r308549);
        double r308551 = y;
        double r308552 = sinh(r308551);
        double r308553 = r308550 * r308552;
        double r308554 = r308553 / r308549;
        return r308554;
}
↓
double f(double x, double y) {
        double r308555 = y;
        double r308556 = sinh(r308555);
        double r308557 = x;
        double r308558 = sin(r308557);
        double r308559 = r308557 / r308558;
        double r308560 = r308556 / r308559;
        return r308560;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.5
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.5

    \[\frac{\sin x \cdot \sinh y}{x}\]
  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 *-un-lft-identity0.8

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

  6. Applied *-un-lft-identity0.8

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

  7. Applied times-frac0.8

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

  8. Applied *-un-lft-identity0.8

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

  9. Applied times-frac0.8

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

  10. Simplified0.8

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(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))