Average Error: 0.0 → 0.0
Time: 24.0s
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 r111171 = x;
        double r111172 = cos(r111171);
        double r111173 = y;
        double r111174 = sinh(r111173);
        double r111175 = r111174 / r111173;
        double r111176 = r111172 * r111175;
        return r111176;
}
↓
double f(double x, double y) {
        double r111177 = x;
        double r111178 = cos(r111177);
        double r111179 = y;
        double r111180 = sinh(r111179);
        double r111181 = r111180 / r111179;
        double r111182 = sqrt(r111181);
        double r111183 = r111182 * r111182;
        double r111184 = r111178 * r111183;
        return r111184;
}

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 2019325 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))