Average Error: 14.2 → 0.1
Time: 24.8s
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 r99527143 = x;
        double r99527144 = sin(r99527143);
        double r99527145 = y;
        double r99527146 = sinh(r99527145);
        double r99527147 = r99527144 * r99527146;
        double r99527148 = r99527147 / r99527143;
        return r99527148;
}
↓
double f(double x, double y) {
        double r99527149 = y;
        double r99527150 = sinh(r99527149);
        double r99527151 = 1.0;
        double r99527152 = x;
        double r99527153 = sin(r99527152);
        double r99527154 = r99527153 / r99527152;
        double r99527155 = r99527151 / r99527154;
        double r99527156 = r99527150 / r99527155;
        return r99527156;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 14.2

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

  2. Taylor expanded around inf 43.2

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

  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 2019173 
(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))