Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5

Average Error: 35.9 → 28.1

Time: 4.8s

Precision: 64

Math

\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \le -0.0:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x}{y \cdot 2} \le 5.25966741260588092 \cdot 10^{125}:\\ \;\;\;\;\left(\sqrt[3]{\frac{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{\frac{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

C

double f(double x, double y) {
        double r602893 = x;
        double r602894 = y;
        double r602895 = 2.0;
        double r602896 = r602894 * r602895;
        double r602897 = r602893 / r602896;
        double r602898 = tan(r602897);
        double r602899 = sin(r602897);
        double r602900 = r602898 / r602899;
        return r602900;
}

↓

double f(double x, double y) {
        double r602901 = x;
        double r602902 = y;
        double r602903 = 2.0;
        double r602904 = r602902 * r602903;
        double r602905 = r602901 / r602904;
        double r602906 = -0.0;
        bool r602907 = r602905 <= r602906;
        double r602908 = 1.0;
        double r602909 = 5.259667412605881e+125;
        bool r602910 = r602905 <= r602909;
        double r602911 = sin(r602905);
        double r602912 = cos(r602905);
        double r602913 = r602911 / r602912;
        double r602914 = r602913 / r602911;
        double r602915 = cbrt(r602914);
        double r602916 = r602915 * r602915;
        double r602917 = tan(r602905);
        double r602918 = r602917 / r602911;
        double r602919 = cbrt(r602918);
        double r602920 = r602916 * r602919;
        double r602921 = r602910 ? r602920 : r602908;
        double r602922 = r602907 ? r602908 : r602921;
        return r602922;
}

Error

Bits error versus x

Bits error versus y

Target

Original	35.9
Target	29.1
Herbie	28.1

\[\begin{array}{l} \mathbf{if}\;y \lt -1.23036909113069936 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.1028524068119138 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (/ x (* y 2.0)) < -0.0 or 5.259667412605881e+125 < (/ x (* y 2.0))

   1. Initial program 43.5

      \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]

   2. Taylor expanded around 0 32.5

      \[\leadsto \color{blue}{1}\]

   if -0.0 < (/ x (* y 2.0)) < 5.259667412605881e+125

   1. Initial program 17.1

      \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
   2. Using strategy rm

   3. Applied add-cube-cbrt 17.1

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}}\]
   4. Using strategy rm

   5. Applied tan-quot 17.1

      \[\leadsto \left(\sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{\frac{\color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\]
   6. Using strategy rm

   7. Applied tan-quot 17.1

      \[\leadsto \left(\sqrt[3]{\frac{\color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}}{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{\frac{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 28.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y \cdot 2} \le -0.0:\\ \;\;\;\;1\\ \mathbf{elif}\;\frac{x}{y \cdot 2} \le 5.25966741260588092 \cdot 10^{125}:\\ \;\;\;\;\left(\sqrt[3]{\frac{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{\frac{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}{\sin \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< y -1.2303690911306994e+114) 1 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2))) (* (sin (/ x (* y 2))) (log (exp (cos (/ x (* y 2))))))) 1))

  (/ (tan (/ x (* y 2))) (sin (/ x (* y 2)))))