Average Error: 0.1 → 0.1
Time: 14.5s
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 r378360 = x;
        double r378361 = cosh(r378360);
        double r378362 = y;
        double r378363 = sin(r378362);
        double r378364 = r378363 / r378362;
        double r378365 = r378361 * r378364;
        return r378365;
}
↓
double f(double x, double y) {
        double r378366 = x;
        double r378367 = cosh(r378366);
        double r378368 = y;
        double r378369 = sin(r378368);
        double r378370 = r378369 / r378368;
        double r378371 = r378367 * r378370;
        return r378371;
}

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 2019305 +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)))