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

Average Error: 35.7 → 28.6

Time: 22.1s

Precision: 64

Math

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

↓

\[\sqrt[3]{\frac{1}{\log \left(e^{{\left(\cos \left(\frac{x}{y \cdot 2}\right)\right)}^{3}}\right)}}\]

C

double f(double x, double y) {
        double r554410 = x;
        double r554411 = y;
        double r554412 = 2.0;
        double r554413 = r554411 * r554412;
        double r554414 = r554410 / r554413;
        double r554415 = tan(r554414);
        double r554416 = sin(r554414);
        double r554417 = r554415 / r554416;
        return r554417;
}

↓

double f(double x, double y) {
        double r554418 = 1.0;
        double r554419 = x;
        double r554420 = y;
        double r554421 = 2.0;
        double r554422 = r554420 * r554421;
        double r554423 = r554419 / r554422;
        double r554424 = cos(r554423);
        double r554425 = 3.0;
        double r554426 = pow(r554424, r554425);
        double r554427 = exp(r554426);
        double r554428 = log(r554427);
        double r554429 = r554418 / r554428;
        double r554430 = cbrt(r554429);
        return r554430;
}

Error

Bits error versus x

Bits error versus y

Target

Original	35.7
Target	29.1
Herbie	28.6

\[\begin{array}{l} \mathbf{if}\;y \lt -1.230369091130699363447511617672816900781 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.102852406811913849731222630299032206502 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

1. Initial program 35.7

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

3. Applied tan-quot 35.7

   \[\leadsto \frac{\color{blue}{\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\cos \left(\frac{x}{y \cdot 2}\right)}}}{\sin \left(\frac{x}{y \cdot 2}\right)}\]

4. Applied associate-/l/ 35.7

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

6. Applied add-cbrt-cube 35.7

   \[\leadsto \frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \color{blue}{\sqrt[3]{\left(\cos \left(\frac{x}{y \cdot 2}\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)}}}\]

7. Applied add-cbrt-cube 50.5

   \[\leadsto \frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\sqrt[3]{\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{\left(\cos \left(\frac{x}{y \cdot 2}\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)}}\]

8. Applied cbrt-unprod 50.5

   \[\leadsto \frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\color{blue}{\sqrt[3]{\left(\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \left(\left(\cos \left(\frac{x}{y \cdot 2}\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)\right)}}}\]

9. Applied add-cbrt-cube 50.3

   \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)}}}{\sqrt[3]{\left(\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \left(\left(\cos \left(\frac{x}{y \cdot 2}\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)\right)}}\]

10. Applied cbrt-undiv 50.3

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)}{\left(\left(\sin \left(\frac{x}{y \cdot 2}\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \sin \left(\frac{x}{y \cdot 2}\right)\right) \cdot \left(\left(\cos \left(\frac{x}{y \cdot 2}\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)\right) \cdot \cos \left(\frac{x}{y \cdot 2}\right)\right)}}}\]

11. Simplified 28.6

    \[\leadsto \sqrt[3]{\color{blue}{\frac{1}{{\left(\cos \left(\frac{x}{y \cdot 2}\right)\right)}^{3}}}}\]
12. Using strategy rm

13. Applied add-log-exp 28.6

    \[\leadsto \sqrt[3]{\frac{1}{\color{blue}{\log \left(e^{{\left(\cos \left(\frac{x}{y \cdot 2}\right)\right)}^{3}}\right)}}}\]

14. Final simplification 28.6

    \[\leadsto \sqrt[3]{\frac{1}{\log \left(e^{{\left(\cos \left(\frac{x}{y \cdot 2}\right)\right)}^{3}}\right)}}\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< y -1.23036909113069936e114) 1 (if (< y -9.1028524068119138e-222) (/ (sin (/ x (* y 2))) (* (sin (/ x (* y 2))) (log (exp (cos (/ x (* y 2))))))) 1))

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