Average Error: 0.0 → 0.0
Time: 4.4s
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 r109000 = x;
        double r109001 = cos(r109000);
        double r109002 = y;
        double r109003 = sinh(r109002);
        double r109004 = r109003 / r109002;
        double r109005 = r109001 * r109004;
        return r109005;
}
↓
double f(double x, double y) {
        double r109006 = x;
        double r109007 = cos(r109006);
        double r109008 = y;
        double r109009 = sinh(r109008);
        double r109010 = r109009 / r109008;
        double r109011 = sqrt(r109010);
        double r109012 = r109011 * r109011;
        double r109013 = r109007 * r109012;
        return r109013;
}

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 2019352 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))