Average Error: 0.0 → 0.0
Time: 12.6s
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 r139653 = x;
        double r139654 = cos(r139653);
        double r139655 = y;
        double r139656 = sinh(r139655);
        double r139657 = r139656 / r139655;
        double r139658 = r139654 * r139657;
        return r139658;
}
↓
double f(double x, double y) {
        double r139659 = x;
        double r139660 = cos(r139659);
        double r139661 = y;
        double r139662 = sinh(r139661);
        double r139663 = r139662 / r139661;
        double r139664 = sqrt(r139663);
        double r139665 = r139660 * r139664;
        double r139666 = r139665 * r139664;
        return r139666;
}

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 2020047 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))