Average Error: 0.1 → 0.1
Time: 5.8s
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 r432293 = x;
        double r432294 = cosh(r432293);
        double r432295 = y;
        double r432296 = sin(r432295);
        double r432297 = r432296 / r432295;
        double r432298 = r432294 * r432297;
        return r432298;
}
↓
double f(double x, double y) {
        double r432299 = x;
        double r432300 = cosh(r432299);
        double r432301 = y;
        double r432302 = sin(r432301);
        double r432303 = r432302 / r432301;
        double r432304 = r432300 * r432303;
        return r432304;
}

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 2020001 +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)))