Average Error: 0.1 → 0.1
Time: 15.8s
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 r471532 = x;
        double r471533 = cosh(r471532);
        double r471534 = y;
        double r471535 = sin(r471534);
        double r471536 = r471535 / r471534;
        double r471537 = r471533 * r471536;
        return r471537;
}
↓
double f(double x, double y) {
        double r471538 = y;
        double r471539 = sin(r471538);
        double r471540 = x;
        double r471541 = cosh(r471540);
        double r471542 = r471539 * r471541;
        double r471543 = r471542 / r471538;
        return r471543;
}

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 2019194 
(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)))