Average Error: 0.0 → 0.1
Time: 13.3s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right)\right)
double f(double x, double y) {
        double r118618 = x;
        double r118619 = sin(r118618);
        double r118620 = y;
        double r118621 = sinh(r118620);
        double r118622 = r118621 / r118620;
        double r118623 = r118619 * r118622;
        return r118623;
}
↓
double f(double x, double y) {
        double r118624 = x;
        double r118625 = sin(r118624);
        double r118626 = y;
        double r118627 = sinh(r118626);
        double r118628 = r118627 / r118626;
        double r118629 = cbrt(r118628);
        double r118630 = r118629 * r118629;
        double r118631 = r118629 * r118630;
        double r118632 = r118625 * r118631;
        return r118632;
}

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-cbrt0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))