Average Error: 0.1 → 0.1
Time: 5.3s
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 r460489 = x;
        double r460490 = cosh(r460489);
        double r460491 = y;
        double r460492 = sin(r460491);
        double r460493 = r460492 / r460491;
        double r460494 = r460490 * r460493;
        return r460494;
}
↓
double f(double x, double y) {
        double r460495 = x;
        double r460496 = cosh(r460495);
        double r460497 = y;
        double r460498 = sin(r460497);
        double r460499 = r460498 / r460497;
        double r460500 = r460496 * r460499;
        return r460500;
}

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 2019353 +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)))