Average Error: 0.0 → 0.0
Time: 32.3s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)
double f(double x, double y) {
        double r114163 = x;
        double r114164 = sin(r114163);
        double r114165 = y;
        double r114166 = sinh(r114165);
        double r114167 = r114166 / r114165;
        double r114168 = r114164 * r114167;
        return r114168;
}
↓
double f(double x, double y) {
        double r114169 = x;
        double r114170 = sin(r114169);
        double r114171 = y;
        double r114172 = sinh(r114171);
        double r114173 = r114172 / r114171;
        double r114174 = sqrt(r114173);
        double r114175 = r114174 * r114174;
        double r114176 = r114170 * r114175;
        return r114176;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

    \[\sin x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019325 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))