Average Error: 0.0 → 0.1
Time: 3.8s
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 r118107 = x;
        double r118108 = cos(r118107);
        double r118109 = y;
        double r118110 = sinh(r118109);
        double r118111 = r118110 / r118109;
        double r118112 = r118108 * r118111;
        return r118112;
}
↓
double f(double x, double y) {
        double r118113 = x;
        double r118114 = cos(r118113);
        double r118115 = y;
        double r118116 = sinh(r118115);
        double r118117 = r118114 * r118116;
        double r118118 = r118117 / r118115;
        return r118118;
}

Error

Bits error versus x

Bits error versus y

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Results

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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)))