Average Error: 0.0 → 0.2
Time: 31.6s
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 r156128 = x;
        double r156129 = sin(r156128);
        double r156130 = y;
        double r156131 = sinh(r156130);
        double r156132 = r156131 / r156130;
        double r156133 = r156129 * r156132;
        return r156133;
}
↓
double f(double x, double y) {
        double r156134 = x;
        double r156135 = sin(r156134);
        double r156136 = y;
        double r156137 = sinh(r156136);
        double r156138 = r156137 / r156136;
        double r156139 = 3.0;
        double r156140 = pow(r156138, r156139);
        double r156141 = cbrt(r156140);
        double r156142 = r156135 * r156141;
        return r156142;
}

Error

Bits error versus x

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-cube41.7

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

  4. Applied add-cbrt-cube41.2

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

  5. Applied cbrt-undiv41.2

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

  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 2019303 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))