Average Error: 0.0 → 0.1
Time: 16.4s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r170896 = x;
        double r170897 = sin(r170896);
        double r170898 = y;
        double r170899 = sinh(r170898);
        double r170900 = r170899 / r170898;
        double r170901 = r170897 * r170900;
        return r170901;
}
↓
double f(double x, double y) {
        double r170902 = x;
        double r170903 = sin(r170902);
        double r170904 = y;
        double r170905 = sinh(r170904);
        double r170906 = r170905 / r170904;
        double r170907 = sqrt(r170906);
        double r170908 = cbrt(r170907);
        double r170909 = r170908 * r170908;
        double r170910 = r170909 * r170908;
        double r170911 = r170903 * r170910;
        double r170912 = r170911 * r170907;
        return r170912;
}

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-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))