Average Error: 0.0 → 0.0
Time: 15.7s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sinh y}{y} \cdot \sin x\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sinh y}{y} \cdot \sin x
double f(double x, double y) {
        double r116677 = x;
        double r116678 = sin(r116677);
        double r116679 = y;
        double r116680 = sinh(r116679);
        double r116681 = r116680 / r116679;
        double r116682 = r116678 * r116681;
        return r116682;
}
↓
double f(double x, double y) {
        double r116683 = y;
        double r116684 = sinh(r116683);
        double r116685 = r116684 / r116683;
        double r116686 = x;
        double r116687 = sin(r116686);
        double r116688 = r116685 * r116687;
        return r116688;
}

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. Using strategy rm

  3. Applied add-cbrt-cube41.7

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

  4. Applied add-cbrt-cube41.2

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

  5. Applied cbrt-undiv41.2

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

  6. Simplified0.2

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))