Average Error: 0.2 → 0.2
Time: 44.6s
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 r18587399 = x;
        double r18587400 = cosh(r18587399);
        double r18587401 = y;
        double r18587402 = sin(r18587401);
        double r18587403 = r18587402 / r18587401;
        double r18587404 = r18587400 * r18587403;
        return r18587404;
}
↓
double f(double x, double y) {
        double r18587405 = x;
        double r18587406 = cosh(r18587405);
        double r18587407 = y;
        double r18587408 = sin(r18587407);
        double r18587409 = r18587408 / r18587407;
        double r18587410 = r18587406 * r18587409;
        return r18587410;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

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

  2. Final simplification0.2

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

Reproduce

herbie shell --seed 2019168 +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)))