Average Error: 0.0 → 0.0
Time: 16.0s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \cos x\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \cos x
double f(double x, double y) {
        double r5772357 = x;
        double r5772358 = cos(r5772357);
        double r5772359 = y;
        double r5772360 = sinh(r5772359);
        double r5772361 = r5772360 / r5772359;
        double r5772362 = r5772358 * r5772361;
        return r5772362;
}
↓
double f(double x, double y) {
        double r5772363 = y;
        double r5772364 = sinh(r5772363);
        double r5772365 = r5772364 / r5772363;
        double r5772366 = sqrt(r5772365);
        double r5772367 = r5772366 * r5772366;
        double r5772368 = x;
        double r5772369 = cos(r5772368);
        double r5772370 = r5772367 * r5772369;
        return r5772370;
}

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

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  (* (cos x) (/ (sinh y) y)))