Average Error: 0.0 → 0.0
Time: 20.8s
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 r8123513 = x;
        double r8123514 = cos(r8123513);
        double r8123515 = y;
        double r8123516 = sinh(r8123515);
        double r8123517 = r8123516 / r8123515;
        double r8123518 = r8123514 * r8123517;
        return r8123518;
}
↓
double f(double x, double y) {
        double r8123519 = y;
        double r8123520 = sinh(r8123519);
        double r8123521 = r8123520 / r8123519;
        double r8123522 = sqrt(r8123521);
        double r8123523 = r8123522 * r8123522;
        double r8123524 = x;
        double r8123525 = cos(r8123524);
        double r8123526 = r8123523 * r8123525;
        return r8123526;
}

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)))