Average Error: 35.7 → 28.4
Time: 14.8s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\frac{1}{\sqrt[3]{\cos \left(\frac{\frac{x}{2}}{y}\right)} \cdot \left(\sqrt[3]{\cos \left(\frac{\frac{x}{2}}{y}\right)} \cdot \sqrt[3]{\cos \left(\frac{\frac{x}{2}}{y}\right)}\right)}\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
\frac{1}{\sqrt[3]{\cos \left(\frac{\frac{x}{2}}{y}\right)} \cdot \left(\sqrt[3]{\cos \left(\frac{\frac{x}{2}}{y}\right)} \cdot \sqrt[3]{\cos \left(\frac{\frac{x}{2}}{y}\right)}\right)}
double f(double x, double y) {
        double r568531 = x;
        double r568532 = y;
        double r568533 = 2.0;
        double r568534 = r568532 * r568533;
        double r568535 = r568531 / r568534;
        double r568536 = tan(r568535);
        double r568537 = sin(r568535);
        double r568538 = r568536 / r568537;
        return r568538;
}
↓
double f(double x, double y) {
        double r568539 = 1.0;
        double r568540 = x;
        double r568541 = 2.0;
        double r568542 = r568540 / r568541;
        double r568543 = y;
        double r568544 = r568542 / r568543;
        double r568545 = cos(r568544);
        double r568546 = cbrt(r568545);
        double r568547 = r568546 * r568546;
        double r568548 = r568546 * r568547;
        double r568549 = r568539 / r568548;
        return r568549;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original35.7
Target28.8
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 35.7

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

  3. Applied tan-quot35.7

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

  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. Simplified35.7

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

  7. Applied clear-num35.7

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

  8. Simplified28.4

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

  10. Applied add-cube-cbrt28.4

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

  11. Final simplification28.4

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

Reproduce

herbie shell --seed 2019174 
(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)))))