Average Error: 0.0 → 0.0
Time: 4.3s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r129315 = x;
        double r129316 = cos(r129315);
        double r129317 = y;
        double r129318 = sinh(r129317);
        double r129319 = r129318 / r129317;
        double r129320 = r129316 * r129319;
        return r129320;
}
↓
double f(double x, double y) {
        double r129321 = x;
        double r129322 = cos(r129321);
        double r129323 = y;
        double r129324 = sinh(r129323);
        double r129325 = r129324 / r129323;
        double r129326 = sqrt(r129325);
        double r129327 = r129322 * r129326;
        double r129328 = r129327 * r129326;
        return r129328;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

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. Applied associate-*r*0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020021 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))