Average Error: 0.2 → 0.3
Time: 6.5s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{1}{\frac{y}{\sin y}}\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{1}{\frac{y}{\sin y}}\right)
double f(double x, double y) {
        double r532853 = x;
        double r532854 = cosh(r532853);
        double r532855 = y;
        double r532856 = sin(r532855);
        double r532857 = r532856 / r532855;
        double r532858 = r532854 * r532857;
        return r532858;
}
↓
double f(double x, double y) {
        double r532859 = x;
        double r532860 = cosh(r532859);
        double r532861 = sqrt(r532860);
        double r532862 = 1.0;
        double r532863 = y;
        double r532864 = sin(r532863);
        double r532865 = r532863 / r532864;
        double r532866 = r532862 / r532865;
        double r532867 = r532861 * r532866;
        double r532868 = r532861 * r532867;
        return r532868;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

    \[\cosh x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.2

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

  4. Applied associate-*l*0.2

    \[\leadsto \color{blue}{\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{\sin y}{y}\right)}\]
  5. Using strategy rm

  6. Applied clear-num0.3

    \[\leadsto \sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\right)\]

  7. Final simplification0.3

    \[\leadsto \sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{1}{\frac{y}{\sin y}}\right)\]

Reproduce

herbie shell --seed 2020035 +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)))