Average Error: 13.7 → 0.1
Time: 35.7s
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 r22484408 = x;
        double r22484409 = sin(r22484408);
        double r22484410 = y;
        double r22484411 = sinh(r22484410);
        double r22484412 = r22484409 * r22484411;
        double r22484413 = r22484412 / r22484408;
        return r22484413;
}
↓
double f(double x, double y) {
        double r22484414 = y;
        double r22484415 = sinh(r22484414);
        double r22484416 = x;
        double r22484417 = sin(r22484416);
        double r22484418 = r22484417 / r22484416;
        double r22484419 = r22484415 * r22484418;
        return r22484419;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original13.7
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.7

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

  2. Taylor expanded around inf 42.8

    \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot \left(\sin x \cdot e^{y}\right) - \frac{1}{2} \cdot \left(\sin x \cdot e^{-y}\right)}{x}}\]

  3. Simplified0.1

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

  5. Applied div-inv0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(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))