Average Error: 0.0 → 0.0
Time: 5.0s
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 r187413 = x;
        double r187414 = cos(r187413);
        double r187415 = y;
        double r187416 = sinh(r187415);
        double r187417 = r187416 / r187415;
        double r187418 = r187414 * r187417;
        return r187418;
}
↓
double f(double x, double y) {
        double r187419 = x;
        double r187420 = cos(r187419);
        double r187421 = y;
        double r187422 = sinh(r187421);
        double r187423 = r187422 / r187421;
        double r187424 = sqrt(r187423);
        double r187425 = r187420 * r187424;
        double r187426 = r187425 * r187424;
        return r187426;
}

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 2020057 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))