Average Error: 0.2 → 0.2
Time: 5.5s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{1}{\frac{y}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{1}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r396984 = x;
        double r396985 = cosh(r396984);
        double r396986 = y;
        double r396987 = sin(r396986);
        double r396988 = r396987 / r396986;
        double r396989 = r396985 * r396988;
        return r396989;
}
↓
double f(double x, double y) {
        double r396990 = x;
        double r396991 = cosh(r396990);
        double r396992 = 1.0;
        double r396993 = y;
        double r396994 = sin(r396993);
        double r396995 = r396993 / r396994;
        double r396996 = r396992 / r396995;
        double r396997 = r396991 * r396996;
        return r396997;
}

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. Using strategy rm

  3. Applied clear-num0.2

    \[\leadsto \cosh x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\]

  4. Final simplification0.2

    \[\leadsto \cosh x \cdot \frac{1}{\frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2020062 +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)))