Average Error: 0.0 → 0.1
Time: 28.6s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}
double f(double x, double y) {
        double r125645 = x;
        double r125646 = cos(r125645);
        double r125647 = y;
        double r125648 = sinh(r125647);
        double r125649 = r125648 / r125647;
        double r125650 = r125646 * r125649;
        return r125650;
}
↓
double f(double x, double y) {
        double r125651 = x;
        double r125652 = cos(r125651);
        double r125653 = y;
        double r125654 = sinh(r125653);
        double r125655 = r125654 / r125653;
        double r125656 = 3.0;
        double r125657 = pow(r125655, r125656);
        double r125658 = cbrt(r125657);
        double r125659 = r125652 * r125658;
        return r125659;
}

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 simplification0.1

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

Reproduce

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