Average Error: 0.0 → 0.0
Time: 25.4s
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 r131734 = x;
        double r131735 = cos(r131734);
        double r131736 = y;
        double r131737 = sinh(r131736);
        double r131738 = r131737 / r131736;
        double r131739 = r131735 * r131738;
        return r131739;
}
↓
double f(double x, double y) {
        double r131740 = x;
        double r131741 = cos(r131740);
        double r131742 = y;
        double r131743 = sinh(r131742);
        double r131744 = r131743 / r131742;
        double r131745 = sqrt(r131744);
        double r131746 = r131745 * r131745;
        double r131747 = r131741 * r131746;
        return r131747;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))