Average Error: 0.1 → 0.1
Time: 15.1s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\sin y \cdot \cosh x}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\sin y \cdot \cosh x}{y}
double f(double x, double y) {
        double r156188 = x;
        double r156189 = cosh(r156188);
        double r156190 = y;
        double r156191 = sin(r156190);
        double r156192 = r156191 / r156190;
        double r156193 = r156189 * r156192;
        return r156193;
}
↓
double f(double x, double y) {
        double r156194 = y;
        double r156195 = sin(r156194);
        double r156196 = x;
        double r156197 = cosh(r156196);
        double r156198 = r156195 * r156197;
        double r156199 = r156198 / r156194;
        return r156199;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019174 
(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)))