Average Error: 0.0 → 0.2
Time: 23.9s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \sqrt[3]{{\left(\frac{\sinh y}{y}\right)}^{3}}
double f(double x, double y) {
        double r133168 = x;
        double r133169 = sin(r133168);
        double r133170 = y;
        double r133171 = sinh(r133170);
        double r133172 = r133171 / r133170;
        double r133173 = r133169 * r133172;
        return r133173;
}
↓
double f(double x, double y) {
        double r133174 = x;
        double r133175 = sin(r133174);
        double r133176 = y;
        double r133177 = sinh(r133176);
        double r133178 = r133177 / r133176;
        double r133179 = 3.0;
        double r133180 = pow(r133178, r133179);
        double r133181 = cbrt(r133180);
        double r133182 = r133175 * r133181;
        return r133182;
}

Error

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Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube41.9

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

  4. Applied add-cbrt-cube41.4

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

  5. Applied cbrt-undiv41.3

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))