Average Error: 14.3 → 0.1
Time: 19.1s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sinh y}{\frac{1}{\frac{\sin x}{x}}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sinh y}{\frac{1}{\frac{\sin x}{x}}}
double f(double x, double y) {
        double r20630051 = x;
        double r20630052 = sin(r20630051);
        double r20630053 = y;
        double r20630054 = sinh(r20630053);
        double r20630055 = r20630052 * r20630054;
        double r20630056 = r20630055 / r20630051;
        return r20630056;
}
↓
double f(double x, double y) {
        double r20630057 = y;
        double r20630058 = sinh(r20630057);
        double r20630059 = 1.0;
        double r20630060 = x;
        double r20630061 = sin(r20630060);
        double r20630062 = r20630061 / r20630060;
        double r20630063 = r20630059 / r20630062;
        double r20630064 = r20630058 / r20630063;
        return r20630064;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.3
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.3

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

  2. Taylor expanded around inf 43.3

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

  3. Simplified0.1

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

  5. Applied clear-num0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(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))