Average Error: 0.1 → 0.1
Time: 21.6s
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 r23521348 = x;
        double r23521349 = cosh(r23521348);
        double r23521350 = y;
        double r23521351 = sin(r23521350);
        double r23521352 = r23521351 / r23521350;
        double r23521353 = r23521349 * r23521352;
        return r23521353;
}
↓
double f(double x, double y) {
        double r23521354 = y;
        double r23521355 = sin(r23521354);
        double r23521356 = x;
        double r23521357 = cosh(r23521356);
        double r23521358 = r23521355 * r23521357;
        double r23521359 = r23521358 / r23521354;
        return r23521359;
}

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. Using strategy rm

  3. Applied associate-*r/0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 +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)))