Average Error: 14.0 → 0.1
Time: 21.6s
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 r24671323 = x;
        double r24671324 = sin(r24671323);
        double r24671325 = y;
        double r24671326 = sinh(r24671325);
        double r24671327 = r24671324 * r24671326;
        double r24671328 = r24671327 / r24671323;
        return r24671328;
}
↓
double f(double x, double y) {
        double r24671329 = y;
        double r24671330 = sinh(r24671329);
        double r24671331 = x;
        double r24671332 = sin(r24671331);
        double r24671333 = r24671331 / r24671332;
        double r24671334 = r24671330 / r24671333;
        return r24671334;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.0
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  2. Taylor expanded around inf 43.6

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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))