Average Error: 0.0 → 0.0
Time: 7.0s
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 r152031 = x;
        double r152032 = cos(r152031);
        double r152033 = y;
        double r152034 = sinh(r152033);
        double r152035 = r152034 / r152033;
        double r152036 = r152032 * r152035;
        return r152036;
}
↓
double f(double x, double y) {
        double r152037 = x;
        double r152038 = cos(r152037);
        double r152039 = y;
        double r152040 = sinh(r152039);
        double r152041 = r152040 / r152039;
        double r152042 = sqrt(r152041);
        double r152043 = r152042 * r152042;
        double r152044 = r152038 * r152043;
        return r152044;
}

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 2019322 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))