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 r129106 = x;
        double r129107 = cos(r129106);
        double r129108 = y;
        double r129109 = sinh(r129108);
        double r129110 = r129109 / r129108;
        double r129111 = r129107 * r129110;
        return r129111;
}
↓
double f(double x, double y) {
        double r129112 = x;
        double r129113 = cos(r129112);
        double r129114 = y;
        double r129115 = sinh(r129114);
        double r129116 = r129113 * r129115;
        double r129117 = r129116 / r129114;
        return r129117;
}

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