Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r479094 = x;
        double r479095 = cosh(r479094);
        double r479096 = y;
        double r479097 = sin(r479096);
        double r479098 = r479097 / r479096;
        double r479099 = r479095 * r479098;
        return r479099;
}
↓
double f(double x, double y) {
        double r479100 = x;
        double r479101 = cosh(r479100);
        double r479102 = y;
        double r479103 = sin(r479102);
        double r479104 = r479103 / r479102;
        double r479105 = r479101 * r479104;
        return r479105;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]

  2. Final simplification0.1

    \[\leadsto \cosh x \cdot \frac{\sin y}{y}\]

Reproduce

herbie shell --seed 2019356 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))