Average Error: 0.1 → 0.2
Time: 25.0s
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 r327075 = x;
        double r327076 = cosh(r327075);
        double r327077 = y;
        double r327078 = sin(r327077);
        double r327079 = r327078 / r327077;
        double r327080 = r327076 * r327079;
        return r327080;
}
↓
double f(double x, double y) {
        double r327081 = x;
        double r327082 = cosh(r327081);
        double r327083 = 1.0;
        double r327084 = y;
        double r327085 = sin(r327084);
        double r327086 = r327084 / r327085;
        double r327087 = r327083 / r327086;
        double r327088 = r327082 * r327087;
        return r327088;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]
  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 2019199 +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)))