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

Average Error: 35.2 → 28.1

Time: 5.3s

Precision: 64

Math

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

↓

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

C

double f(double x, double y) {
        double r632728 = x;
        double r632729 = y;
        double r632730 = 2.0;
        double r632731 = r632729 * r632730;
        double r632732 = r632728 / r632731;
        double r632733 = tan(r632732);
        double r632734 = sin(r632732);
        double r632735 = r632733 / r632734;
        return r632735;
}

↓

double f(double x, double y) {
        double r632736 = 1.0;
        double r632737 = x;
        double r632738 = y;
        double r632739 = 2.0;
        double r632740 = r632738 * r632739;
        double r632741 = r632737 / r632740;
        double r632742 = cos(r632741);
        double r632743 = cbrt(r632742);
        double r632744 = r632743 * r632743;
        double r632745 = r632736 / r632744;
        double r632746 = exp(r632742);
        double r632747 = log(r632746);
        double r632748 = cbrt(r632747);
        double r632749 = r632736 / r632748;
        double r632750 = r632745 * r632749;
        return r632750;
}

Error

Bits error versus x

Bits error versus y

Target

Original	35.2
Target	28.6
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. Initial program 35.2

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

3. Applied tan-quot 35.2

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

5. Applied add-cube-cbrt 35.7

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

6. Applied add-cube-cbrt 35.7

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

7. Applied add-cube-cbrt 35.2

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

8. Applied times-frac 35.2

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

9. Applied times-frac 35.2

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

10. Simplified 35.2

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

11. Simplified 28.1

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

13. Applied add-log-exp 28.1

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

14. Final simplification 28.1

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

Reproduce

herbie shell --seed 2020056 
(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)))))