Average Error: 0.0 → 0.1
Time: 24.1s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sin x}{\sqrt[3]{\frac{y}{\sinh y} \cdot \left(\frac{y}{\sinh y} \cdot \frac{y}{\sinh y}\right)}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\sqrt[3]{\frac{y}{\sinh y} \cdot \left(\frac{y}{\sinh y} \cdot \frac{y}{\sinh y}\right)}}
double f(double x, double y) {
        double r9092123 = x;
        double r9092124 = sin(r9092123);
        double r9092125 = y;
        double r9092126 = sinh(r9092125);
        double r9092127 = r9092126 / r9092125;
        double r9092128 = r9092124 * r9092127;
        return r9092128;
}
↓
double f(double x, double y) {
        double r9092129 = x;
        double r9092130 = sin(r9092129);
        double r9092131 = y;
        double r9092132 = sinh(r9092131);
        double r9092133 = r9092131 / r9092132;
        double r9092134 = r9092133 * r9092133;
        double r9092135 = r9092133 * r9092134;
        double r9092136 = cbrt(r9092135);
        double r9092137 = r9092130 / r9092136;
        return r9092137;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around inf 58.7

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

  3. Simplified0.0

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

  5. Applied add-cbrt-cube39.9

    \[\leadsto \frac{\sin x}{\frac{y}{\color{blue}{\sqrt[3]{\left(\sinh y \cdot \sinh y\right) \cdot \sinh y}}}}\]

  6. Applied add-cbrt-cube40.3

    \[\leadsto \frac{\sin x}{\frac{\color{blue}{\sqrt[3]{\left(y \cdot y\right) \cdot y}}}{\sqrt[3]{\left(\sinh y \cdot \sinh y\right) \cdot \sinh y}}}\]

  7. Applied cbrt-undiv40.3

    \[\leadsto \frac{\sin x}{\color{blue}{\sqrt[3]{\frac{\left(y \cdot y\right) \cdot y}{\left(\sinh y \cdot \sinh y\right) \cdot \sinh y}}}}\]

  8. Simplified0.1

    \[\leadsto \frac{\sin x}{\sqrt[3]{\color{blue}{\left(\frac{y}{\sinh y} \cdot \frac{y}{\sinh y}\right) \cdot \frac{y}{\sinh y}}}}\]

  9. Final simplification0.1

    \[\leadsto \frac{\sin x}{\sqrt[3]{\frac{y}{\sinh y} \cdot \left(\frac{y}{\sinh y} \cdot \frac{y}{\sinh y}\right)}}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))