Average Error: 0.0 → 0.1
Time: 4.1s
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 r202162 = x;
        double r202163 = cos(r202162);
        double r202164 = y;
        double r202165 = sinh(r202164);
        double r202166 = r202165 / r202164;
        double r202167 = r202163 * r202166;
        return r202167;
}
↓
double f(double x, double y) {
        double r202168 = x;
        double r202169 = cos(r202168);
        double r202170 = y;
        double r202171 = sinh(r202170);
        double r202172 = r202171 / r202170;
        double r202173 = 3.0;
        double r202174 = pow(r202172, r202173);
        double r202175 = cbrt(r202174);
        double r202176 = r202169 * r202175;
        return r202176;
}

Error

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