Average Error: 0.0 → 0.1
Time: 4.4s
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 r134997 = x;
        double r134998 = cos(r134997);
        double r134999 = y;
        double r135000 = sinh(r134999);
        double r135001 = r135000 / r134999;
        double r135002 = r134998 * r135001;
        return r135002;
}
↓
double f(double x, double y) {
        double r135003 = x;
        double r135004 = cos(r135003);
        double r135005 = y;
        double r135006 = sinh(r135005);
        double r135007 = r135006 / r135005;
        double r135008 = 3.0;
        double r135009 = pow(r135007, r135008);
        double r135010 = cbrt(r135009);
        double r135011 = r135004 * r135010;
        return r135011;
}

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-cube41.8

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

  4. Applied add-cbrt-cube41.3

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

  5. Applied cbrt-undiv41.3

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

  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 2020056 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))