Average Error: 0.0 → 0.0
Time: 20.7s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \cos x\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \cos x
double f(double x, double y) {
        double r5873817 = x;
        double r5873818 = cos(r5873817);
        double r5873819 = y;
        double r5873820 = sinh(r5873819);
        double r5873821 = r5873820 / r5873819;
        double r5873822 = r5873818 * r5873821;
        return r5873822;
}
↓
double f(double x, double y) {
        double r5873823 = y;
        double r5873824 = sinh(r5873823);
        double r5873825 = r5873824 / r5873823;
        double r5873826 = sqrt(r5873825);
        double r5873827 = sqrt(r5873826);
        double r5873828 = r5873826 * r5873827;
        double r5873829 = r5873828 * r5873827;
        double r5873830 = x;
        double r5873831 = cos(r5873830);
        double r5873832 = r5873829 * r5873831;
        return r5873832;
}

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-sqr-sqrt0.0

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

  5. Applied add-sqr-sqrt0.0

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

  6. Applied sqrt-prod0.0

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

  7. Applied associate-*l*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))