Average Error: 0.0 → 0.0
Time: 16.0s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right)
double f(double x, double y) {
        double r118381 = x;
        double r118382 = cos(r118381);
        double r118383 = y;
        double r118384 = sinh(r118383);
        double r118385 = r118384 / r118383;
        double r118386 = r118382 * r118385;
        return r118386;
}
↓
double f(double x, double y) {
        double r118387 = y;
        double r118388 = sinh(r118387);
        double r118389 = r118388 / r118387;
        double r118390 = sqrt(r118389);
        double r118391 = x;
        double r118392 = cos(r118391);
        double r118393 = r118390 * r118392;
        double r118394 = r118390 * r118393;
        return r118394;
}

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

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))