Average Error: 0.1 → 0.1
Time: 17.0s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\cosh x \cdot \sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\cosh x \cdot \sin y}{y}
double f(double x, double y) {
        double r462292 = x;
        double r462293 = cosh(r462292);
        double r462294 = y;
        double r462295 = sin(r462294);
        double r462296 = r462295 / r462294;
        double r462297 = r462293 * r462296;
        return r462297;
}
↓
double f(double x, double y) {
        double r462298 = x;
        double r462299 = cosh(r462298);
        double r462300 = y;
        double r462301 = sin(r462300);
        double r462302 = r462299 * r462301;
        double r462303 = r462302 / r462300;
        return r462303;
}

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. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"

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

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