Average Error: 0.0 → 0.0
Time: 15.9s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \cos x\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\left(\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}\right) \cdot \cos x\right) \cdot \sqrt[3]{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r105948 = x;
        double r105949 = cos(r105948);
        double r105950 = y;
        double r105951 = sinh(r105950);
        double r105952 = r105951 / r105950;
        double r105953 = r105949 * r105952;
        return r105953;
}
↓
double f(double x, double y) {
        double r105954 = y;
        double r105955 = sinh(r105954);
        double r105956 = r105955 / r105954;
        double r105957 = cbrt(r105956);
        double r105958 = r105957 * r105957;
        double r105959 = x;
        double r105960 = cos(r105959);
        double r105961 = r105958 * r105960;
        double r105962 = r105961 * r105957;
        return r105962;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt0.0

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

  4. Applied associate-*r*0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

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