Average Error: 0.0 → 0.0
Time: 18.1s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sin x\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \sin x\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r130941 = x;
        double r130942 = sin(r130941);
        double r130943 = y;
        double r130944 = sinh(r130943);
        double r130945 = r130944 / r130943;
        double r130946 = r130942 * r130945;
        return r130946;
}
↓
double f(double x, double y) {
        double r130947 = y;
        double r130948 = sinh(r130947);
        double r130949 = r130948 / r130947;
        double r130950 = cbrt(r130949);
        double r130951 = r130950 * r130950;
        double r130952 = x;
        double r130953 = sin(r130952);
        double r130954 = r130951 * r130953;
        double r130955 = r130954 * r130950;
        return r130955;
}

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-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. Applied associate-*r*0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))