Average Error: 0.0 → 0.0
Time: 5.4s
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 r128775 = x;
        double r128776 = sin(r128775);
        double r128777 = y;
        double r128778 = sinh(r128777);
        double r128779 = r128778 / r128777;
        double r128780 = r128776 * r128779;
        return r128780;
}
↓
double f(double x, double y) {
        double r128781 = x;
        double r128782 = sin(r128781);
        double r128783 = y;
        double r128784 = sinh(r128783);
        double r128785 = r128784 / r128783;
        double r128786 = sqrt(r128785);
        double r128787 = r128786 * r128786;
        double r128788 = r128782 * r128787;
        return r128788;
}

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 2019346 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))