Average Error: 0.1 → 0.2
Time: 14.9s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\sin y}{\frac{y}{\cosh x}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\sin y}{\frac{y}{\cosh x}}
double f(double x, double y) {
        double r400233 = x;
        double r400234 = cosh(r400233);
        double r400235 = y;
        double r400236 = sin(r400235);
        double r400237 = r400236 / r400235;
        double r400238 = r400234 * r400237;
        return r400238;
}
↓
double f(double x, double y) {
        double r400239 = y;
        double r400240 = sin(r400239);
        double r400241 = x;
        double r400242 = cosh(r400241);
        double r400243 = r400239 / r400242;
        double r400244 = r400240 / r400243;
        return r400244;
}

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 add-cube-cbrt0.2

    \[\leadsto \color{blue}{\left(\left(\sqrt[3]{\cosh x} \cdot \sqrt[3]{\cosh x}\right) \cdot \sqrt[3]{\cosh x}\right)} \cdot \frac{\sin y}{y}\]

  4. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\left(\sqrt[3]{\cosh x} \cdot \sqrt[3]{\cosh x}\right) \cdot \left(\sqrt[3]{\cosh x} \cdot \frac{\sin y}{y}\right)}\]

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019291 
(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)))