Average Error: 0.0 → 0.0
Time: 18.0s
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 r6504363 = x;
        double r6504364 = cos(r6504363);
        double r6504365 = y;
        double r6504366 = sinh(r6504365);
        double r6504367 = r6504366 / r6504365;
        double r6504368 = r6504364 * r6504367;
        return r6504368;
}
↓
double f(double x, double y) {
        double r6504369 = y;
        double r6504370 = sinh(r6504369);
        double r6504371 = r6504370 / r6504369;
        double r6504372 = sqrt(r6504371);
        double r6504373 = r6504372 * r6504372;
        double r6504374 = x;
        double r6504375 = cos(r6504374);
        double r6504376 = r6504373 * r6504375;
        return r6504376;
}

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