Average Error: 0.0 → 0.0
Time: 25.3s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)
double f(double x, double y) {
        double r109045 = x;
        double r109046 = cos(r109045);
        double r109047 = y;
        double r109048 = sinh(r109047);
        double r109049 = r109048 / r109047;
        double r109050 = r109046 * r109049;
        return r109050;
}
↓
double f(double x, double y) {
        double r109051 = x;
        double r109052 = cos(r109051);
        double r109053 = y;
        double r109054 = sinh(r109053);
        double r109055 = r109054 / r109053;
        double r109056 = sqrt(r109055);
        double r109057 = r109056 * r109056;
        double r109058 = r109052 * r109057;
        return r109058;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))