Average Error: 0.2 → 0.2
Time: 5.0s
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 r436156 = x;
        double r436157 = cosh(r436156);
        double r436158 = y;
        double r436159 = sin(r436158);
        double r436160 = r436159 / r436158;
        double r436161 = r436157 * r436160;
        return r436161;
}
↓
double f(double x, double y) {
        double r436162 = x;
        double r436163 = cosh(r436162);
        double r436164 = 1.0;
        double r436165 = y;
        double r436166 = sin(r436165);
        double r436167 = r436165 / r436166;
        double r436168 = r436164 / r436167;
        double r436169 = r436163 * r436168;
        return r436169;
}

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 
(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)))