Average Error: 13.8 → 0.1
Time: 14.6s
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 r403486 = x;
        double r403487 = sin(r403486);
        double r403488 = y;
        double r403489 = sinh(r403488);
        double r403490 = r403487 * r403489;
        double r403491 = r403490 / r403486;
        return r403491;
}
↓
double f(double x, double y) {
        double r403492 = x;
        double r403493 = sin(r403492);
        double r403494 = r403493 / r403492;
        double r403495 = y;
        double r403496 = sinh(r403495);
        double r403497 = r403494 * r403496;
        return r403497;
}

Error

Bits error versus x

Bits error versus y

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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 *-un-lft-identity13.8

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  7. Applied clear-num0.9

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019297 
(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))