Average Error: 0.0 → 0.0
Time: 4.5s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r88787 = x;
        double r88788 = cos(r88787);
        double r88789 = y;
        double r88790 = sinh(r88789);
        double r88791 = r88790 / r88789;
        double r88792 = r88788 * r88791;
        return r88792;
}
↓
double f(double x, double y) {
        double r88793 = x;
        double r88794 = cos(r88793);
        double r88795 = y;
        double r88796 = sinh(r88795);
        double r88797 = r88796 / r88795;
        double r88798 = sqrt(r88797);
        double r88799 = r88794 * r88798;
        double r88800 = r88799 * r88798;
        return r88800;
}

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

    \[\cos x \cdot \frac{\sinh y}{y}\]
  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. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))