Average Error: 35.8 → 28.5
Time: 5.7s
Precision: 64
\[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
↓
\[\log \left({\left(e^{\frac{2}{\log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}\right)}^{\frac{1}{2}}\right)\]
\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}
↓
\log \left({\left(e^{\frac{2}{\log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}}\right)}^{\frac{1}{2}}\right)
double f(double x, double y) {
        double r548216 = x;
        double r548217 = y;
        double r548218 = 2.0;
        double r548219 = r548217 * r548218;
        double r548220 = r548216 / r548219;
        double r548221 = tan(r548220);
        double r548222 = sin(r548220);
        double r548223 = r548221 / r548222;
        return r548223;
}
↓
double f(double x, double y) {
        double r548224 = 2.0;
        double r548225 = x;
        double r548226 = y;
        double r548227 = 2.0;
        double r548228 = r548226 * r548227;
        double r548229 = r548225 / r548228;
        double r548230 = cos(r548229);
        double r548231 = exp(r548230);
        double r548232 = log(r548231);
        double r548233 = r548224 / r548232;
        double r548234 = exp(r548233);
        double r548235 = 0.5;
        double r548236 = pow(r548234, r548235);
        double r548237 = log(r548236);
        return r548237;
}

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
Target29.0
Herbie28.5
\[\begin{array}{l} \mathbf{if}\;y \lt -1.230369091130699363447511617672816900781 \cdot 10^{114}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \lt -9.102852406811913849731222630299032206502 \cdot 10^{-222}:\\ \;\;\;\;\frac{\sin \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right) \cdot \log \left(e^{\cos \left(\frac{x}{y \cdot 2}\right)}\right)}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]

Derivation

  1. Initial program 35.8

    \[\frac{\tan \left(\frac{x}{y \cdot 2}\right)}{\sin \left(\frac{x}{y \cdot 2}\right)}\]
  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. Applied associate-/l/35.8

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

  6. Applied add-log-exp35.8

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

  7. Simplified28.5

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

  9. Applied add-log-exp28.5

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

  10. Final simplification28.5

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

Reproduce

herbie shell --seed 2019362 
(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)))))