Average Error: 0.1 → 0.1
Time: 5.6s
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 r479102 = x;
        double r479103 = cosh(r479102);
        double r479104 = y;
        double r479105 = sin(r479104);
        double r479106 = r479105 / r479104;
        double r479107 = r479103 * r479106;
        return r479107;
}
↓
double f(double x, double y) {
        double r479108 = x;
        double r479109 = cosh(r479108);
        double r479110 = y;
        double r479111 = sin(r479110);
        double r479112 = r479111 / r479110;
        double r479113 = r479109 * r479112;
        return r479113;
}

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 2020046 +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)))