Average Error: 0.0 → 0.1
Time: 20.9s
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 r96118 = x;
        double r96119 = sin(r96118);
        double r96120 = y;
        double r96121 = sinh(r96120);
        double r96122 = r96121 / r96120;
        double r96123 = r96119 * r96122;
        return r96123;
}
↓
double f(double x, double y) {
        double r96124 = x;
        double r96125 = sin(r96124);
        double r96126 = y;
        double r96127 = sinh(r96126);
        double r96128 = r96127 / r96126;
        double r96129 = 3.0;
        double r96130 = pow(r96128, r96129);
        double r96131 = cbrt(r96130);
        double r96132 = r96125 * r96131;
        return r96132;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))