Average Error: 0.0 → 0.0
Time: 16.8s
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 r10577448 = x;
        double r10577449 = cos(r10577448);
        double r10577450 = y;
        double r10577451 = sinh(r10577450);
        double r10577452 = r10577451 / r10577450;
        double r10577453 = r10577449 * r10577452;
        return r10577453;
}
↓
double f(double x, double y) {
        double r10577454 = x;
        double r10577455 = cos(r10577454);
        double r10577456 = y;
        double r10577457 = sinh(r10577456);
        double r10577458 = r10577457 / r10577456;
        double r10577459 = sqrt(r10577458);
        double r10577460 = r10577459 * r10577459;
        double r10577461 = r10577455 * r10577460;
        return r10577461;
}

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 2019174 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))