Average Error: 0.0 → 0.0
Time: 23.6s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sin x\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sin x
double f(double x, double y) {
        double r6014616 = x;
        double r6014617 = sin(r6014616);
        double r6014618 = y;
        double r6014619 = sinh(r6014618);
        double r6014620 = r6014619 / r6014618;
        double r6014621 = r6014617 * r6014620;
        return r6014621;
}
↓
double f(double x, double y) {
        double r6014622 = y;
        double r6014623 = sinh(r6014622);
        double r6014624 = r6014623 / r6014622;
        double r6014625 = sqrt(r6014624);
        double r6014626 = r6014625 * r6014625;
        double r6014627 = x;
        double r6014628 = sin(r6014627);
        double r6014629 = r6014626 * r6014628;
        return r6014629;
}

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

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))