Average Error: 0.0 → 0.0
Time: 7.9s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)
double f(double x, double y) {
        double r177111 = x;
        double r177112 = sin(r177111);
        double r177113 = y;
        double r177114 = sinh(r177113);
        double r177115 = r177114 / r177113;
        double r177116 = r177112 * r177115;
        return r177116;
}
↓
double f(double x, double y) {
        double r177117 = x;
        double r177118 = sin(r177117);
        double r177119 = y;
        double r177120 = sinh(r177119);
        double r177121 = r177120 / r177119;
        double r177122 = cbrt(r177121);
        double r177123 = r177122 * r177122;
        double r177124 = r177123 * r177122;
        double r177125 = r177118 * r177124;
        return r177125;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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-cube-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020083 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))