Average Error: 35.4 → 28.4
Time: 23.9s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}} \cdot {\left(\sqrt[3]{\sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}}\right)}^{6}\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
\sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}} \cdot {\left(\sqrt[3]{\sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}}\right)}^{6}
double f(double x, double y) {
        double r447560 = x;
        double r447561 = y;
        double r447562 = 2.0;
        double r447563 = r447561 * r447562;
        double r447564 = r447560 / r447563;
        double r447565 = tan(r447564);
        double r447566 = sin(r447564);
        double r447567 = r447565 / r447566;
        return r447567;
}
↓
double f(double x, double y) {
        double r447568 = 1.0;
        double r447569 = x;
        double r447570 = y;
        double r447571 = 2.0;
        double r447572 = r447570 * r447571;
        double r447573 = r447569 / r447572;
        double r447574 = cos(r447573);
        double r447575 = r447568 / r447574;
        double r447576 = cbrt(r447575);
        double r447577 = cbrt(r447576);
        double r447578 = 6.0;
        double r447579 = pow(r447577, r447578);
        double r447580 = r447576 * r447579;
        return r447580;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.4
Target28.9
Herbie28.4
\[\begin{array}{l} \mathbf{if}\;y \lt -1.230369091130699363447511617672816900781 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.102852406811913849731222630299032206502 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Initial program 35.4

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

  3. Applied tan-quot35.4

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

  4. Applied associate-/l/35.4

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

  6. Applied add-cube-cbrt35.4

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

  7. Simplified35.4

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

  8. Simplified28.4

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

  10. Applied *-un-lft-identity28.4

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

  11. Applied cbrt-prod28.4

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

  12. Applied associate-*l*28.4

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

  13. Simplified28.4

    \[\leadsto \left(\sqrt[3]{1} \cdot \color{blue}{{\left(\sqrt[3]{\sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}}\right)}^{6}}\right) \cdot \sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}\]

  14. Final simplification28.4

    \[\leadsto \sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}} \cdot {\left(\sqrt[3]{\sqrt[3]{\frac{1}{\cos \left(\frac{x}{y \cdot 2}\right)}}}\right)}^{6}\]

Reproduce

herbie shell --seed 2019326 
(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)))))