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

Average Error: 35.9 → 28.1

Time: 4.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r785401 = x;
        double r785402 = y;
        double r785403 = 2.0;
        double r785404 = r785402 * r785403;
        double r785405 = r785401 / r785404;
        double r785406 = tan(r785405);
        double r785407 = sin(r785405);
        double r785408 = r785406 / r785407;
        return r785408;
}

↓

double f(double x, double y) {
        double r785409 = x;
        double r785410 = y;
        double r785411 = 2.0;
        double r785412 = r785410 * r785411;
        double r785413 = r785409 / r785412;
        double r785414 = -0.0;
        bool r785415 = r785413 <= r785414;
        double r785416 = 1.0;
        double r785417 = 5.259667412605881e+125;
        bool r785418 = r785413 <= r785417;
        double r785419 = sin(r785413);
        double r785420 = cos(r785413);
        double r785421 = r785419 / r785420;
        double r785422 = r785421 / r785419;
        double r785423 = cbrt(r785422);
        double r785424 = tan(r785413);
        double r785425 = r785424 / r785419;
        double r785426 = cbrt(r785425);
        double r785427 = r785423 * r785426;
        double r785428 = r785427 * r785423;
        double r785429 = r785418 ? r785428 : r785416;
        double r785430 = r785415 ? r785416 : r785429;
        return r785430;
}

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

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

   7. Applied tan-quot 17.1

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

4. Final simplification 28.1

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

Reproduce

herbie shell --seed 2020062 
(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)))))