Average Error: 16.6 → 12.3
Time: 10.1s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \frac{1}{\frac{\frac{F}{\tan \left(\pi \cdot \ell\right)}}{\sqrt{1}}}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \frac{1}{\frac{\frac{F}{\tan \left(\pi \cdot \ell\right)}}{\sqrt{1}}}
double f(double F, double l) {
        double r18290 = atan2(1.0, 0.0);
        double r18291 = l;
        double r18292 = r18290 * r18291;
        double r18293 = 1.0;
        double r18294 = F;
        double r18295 = r18294 * r18294;
        double r18296 = r18293 / r18295;
        double r18297 = tan(r18292);
        double r18298 = r18296 * r18297;
        double r18299 = r18292 - r18298;
        return r18299;
}
↓
double f(double F, double l) {
        double r18300 = atan2(1.0, 0.0);
        double r18301 = l;
        double r18302 = r18300 * r18301;
        double r18303 = 1.0;
        double r18304 = sqrt(r18303);
        double r18305 = F;
        double r18306 = r18304 / r18305;
        double r18307 = 1.0;
        double r18308 = tan(r18302);
        double r18309 = r18305 / r18308;
        double r18310 = r18309 / r18304;
        double r18311 = r18307 / r18310;
        double r18312 = r18306 * r18311;
        double r18313 = r18302 - r18312;
        return r18313;
}

Error

Bits error versus F

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 16.6

    \[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt16.6

    \[\leadsto \pi \cdot \ell - \frac{\color{blue}{\sqrt{1} \cdot \sqrt{1}}}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]

  4. Applied times-frac16.6

    \[\leadsto \pi \cdot \ell - \color{blue}{\left(\frac{\sqrt{1}}{F} \cdot \frac{\sqrt{1}}{F}\right)} \cdot \tan \left(\pi \cdot \ell\right)\]

  5. Applied associate-*l*12.3

    \[\leadsto \pi \cdot \ell - \color{blue}{\frac{\sqrt{1}}{F} \cdot \left(\frac{\sqrt{1}}{F} \cdot \tan \left(\pi \cdot \ell\right)\right)}\]
  6. Using strategy rm

  7. Applied associate-*l/12.3

    \[\leadsto \pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \color{blue}{\frac{\sqrt{1} \cdot \tan \left(\pi \cdot \ell\right)}{F}}\]
  8. Using strategy rm

  9. Applied associate-/l*12.3

    \[\leadsto \pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \color{blue}{\frac{\sqrt{1}}{\frac{F}{\tan \left(\pi \cdot \ell\right)}}}\]
  10. Using strategy rm

  11. Applied clear-num12.3

    \[\leadsto \pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \color{blue}{\frac{1}{\frac{\frac{F}{\tan \left(\pi \cdot \ell\right)}}{\sqrt{1}}}}\]

  12. Final simplification12.3

    \[\leadsto \pi \cdot \ell - \frac{\sqrt{1}}{F} \cdot \frac{1}{\frac{\frac{F}{\tan \left(\pi \cdot \ell\right)}}{\sqrt{1}}}\]

Reproduce

herbie shell --seed 2020035 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  :precision binary64
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))