Average Error: 35.8 → 28.5
Time: 21.6s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\left(\sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
\left(\sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}} \cdot \sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}\right) \cdot \sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}
double f(double x, double y) {
        double r469728 = x;
        double r469729 = y;
        double r469730 = 2.0;
        double r469731 = r469729 * r469730;
        double r469732 = r469728 / r469731;
        double r469733 = tan(r469732);
        double r469734 = sin(r469732);
        double r469735 = r469733 / r469734;
        return r469735;
}
↓
double f(double x, double y) {
        double r469736 = 1.0;
        double r469737 = x;
        double r469738 = y;
        double r469739 = 2.0;
        double r469740 = r469738 * r469739;
        double r469741 = r469737 / r469740;
        double r469742 = cos(r469741);
        double r469743 = r469736 / r469742;
        double r469744 = cbrt(r469743);
        double r469745 = r469744 * r469744;
        double r469746 = r469745 * r469744;
        return r469746;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.8
Target29.1
Herbie28.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.23036909113069936 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.1028524068119138 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Initial program 35.8

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

  3. Applied tan-quot35.8

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

  5. Applied add-cube-cbrt35.8

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

  6. Simplified35.8

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

  7. Simplified28.5

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

  8. Final simplification28.5

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y)
  :name "Diagrams.TwoD.Layout.CirclePacking:approxRadius from diagrams-contrib-1.3.0.5"

  :herbie-target
  (if (< y -1.2303690911306994e+114) 1.0 (if (< y -9.102852406811914e-222) (/ (sin (/ x (* y 2.0))) (* (sin (/ x (* y 2.0))) (log (exp (cos (/ x (* y 2.0))))))) 1.0))

  (/ (tan (/ x (* y 2.0))) (sin (/ x (* y 2.0)))))