Average Error: 0.1 → 0.1
Time: 20.2s
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 r27430523 = x;
        double r27430524 = cosh(r27430523);
        double r27430525 = y;
        double r27430526 = sin(r27430525);
        double r27430527 = r27430526 / r27430525;
        double r27430528 = r27430524 * r27430527;
        return r27430528;
}
↓
double f(double x, double y) {
        double r27430529 = x;
        double r27430530 = cosh(r27430529);
        double r27430531 = y;
        double r27430532 = sin(r27430531);
        double r27430533 = r27430532 / r27430531;
        double r27430534 = r27430530 * r27430533;
        return r27430534;
}

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 2019174 +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)))