Average Error: 0.2 → 0.2
Time: 28.3s
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 r590302 = x;
        double r590303 = cosh(r590302);
        double r590304 = y;
        double r590305 = sin(r590304);
        double r590306 = r590305 / r590304;
        double r590307 = r590303 * r590306;
        return r590307;
}
↓
double f(double x, double y) {
        double r590308 = x;
        double r590309 = cosh(r590308);
        double r590310 = y;
        double r590311 = sin(r590310);
        double r590312 = r590311 / r590310;
        double r590313 = r590309 * r590312;
        return r590313;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 +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)))