Average Error: 0.0 → 0.1
Time: 5.1s
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 r89677 = x;
        double r89678 = cos(r89677);
        double r89679 = y;
        double r89680 = sinh(r89679);
        double r89681 = r89680 / r89679;
        double r89682 = r89678 * r89681;
        return r89682;
}
↓
double f(double x, double y) {
        double r89683 = x;
        double r89684 = cos(r89683);
        double r89685 = y;
        double r89686 = sinh(r89685);
        double r89687 = r89686 / r89685;
        double r89688 = 3.0;
        double r89689 = pow(r89687, r89688);
        double r89690 = cbrt(r89689);
        double r89691 = r89684 * r89690;
        return r89691;
}

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-cube40.7

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

  4. Applied add-cbrt-cube40.2

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

  5. Applied cbrt-undiv40.2

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

  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 2020034 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))