Average Error: 0.0 → 0.1
Time: 4.1s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\cos x \cdot \sinh y}{y}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\cos x \cdot \sinh y}{y}
double f(double x, double y) {
        double r155673 = x;
        double r155674 = cos(r155673);
        double r155675 = y;
        double r155676 = sinh(r155675);
        double r155677 = r155676 / r155675;
        double r155678 = r155674 * r155677;
        return r155678;
}
↓
double f(double x, double y) {
        double r155679 = x;
        double r155680 = cos(r155679);
        double r155681 = y;
        double r155682 = sinh(r155681);
        double r155683 = r155680 * r155682;
        double r155684 = r155683 / r155681;
        return r155684;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\cos x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied associate-*r/0.1

    \[\leadsto \color{blue}{\frac{\cos x \cdot \sinh y}{y}}\]

  4. Final simplification0.1

    \[\leadsto \frac{\cos x \cdot \sinh y}{y}\]

Reproduce

herbie shell --seed 2020060 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))