Average Error: 0.0 → 0.0
Time: 12.8s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sinh y}{y} \cdot \cos x\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\sinh y}{y} \cdot \cos x
double f(double x, double y) {
        double r161825 = x;
        double r161826 = cos(r161825);
        double r161827 = y;
        double r161828 = sinh(r161827);
        double r161829 = r161828 / r161827;
        double r161830 = r161826 * r161829;
        return r161830;
}
↓
double f(double x, double y) {
        double r161831 = y;
        double r161832 = sinh(r161831);
        double r161833 = r161832 / r161831;
        double r161834 = x;
        double r161835 = cos(r161834);
        double r161836 = r161833 * r161835;
        return r161836;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

    \[\cos x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube41.7

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

  4. Applied add-cbrt-cube41.2

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

  5. Applied cbrt-undiv41.2

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

  6. Simplified0.1

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

  7. Final simplification0.0

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

Reproduce

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