Average Error: 0.0 → 0.0
Time: 15.5s
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 r10272314 = x;
        double r10272315 = cos(r10272314);
        double r10272316 = y;
        double r10272317 = sinh(r10272316);
        double r10272318 = r10272317 / r10272316;
        double r10272319 = r10272315 * r10272318;
        return r10272319;
}
↓
double f(double x, double y) {
        double r10272320 = x;
        double r10272321 = cos(r10272320);
        double r10272322 = y;
        double r10272323 = sinh(r10272322);
        double r10272324 = r10272323 / r10272322;
        double r10272325 = sqrt(r10272324);
        double r10272326 = r10272325 * r10272325;
        double r10272327 = r10272321 * r10272326;
        return r10272327;
}

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