Average Error: 8.5 → 0.7
Time: 44.1s
Precision: 64
\[\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)\]
↓
\[\pi \cdot \ell - \left(\frac{1}{F} \cdot \tan \left(\pi \cdot \ell\right)\right) \cdot \frac{1}{F}\]
\pi \cdot \ell - \frac{1}{F \cdot F} \cdot \tan \left(\pi \cdot \ell\right)
↓
\pi \cdot \ell - \left(\frac{1}{F} \cdot \tan \left(\pi \cdot \ell\right)\right) \cdot \frac{1}{F}
double f(double F, double l) {
        double r696908 = atan2(1.0, 0.0);
        double r696909 = l;
        double r696910 = r696908 * r696909;
        double r696911 = 1.0;
        double r696912 = F;
        double r696913 = r696912 * r696912;
        double r696914 = r696911 / r696913;
        double r696915 = tan(r696910);
        double r696916 = r696914 * r696915;
        double r696917 = r696910 - r696916;
        return r696917;
}
↓
double f(double F, double l) {
        double r696918 = atan2(1.0, 0.0);
        double r696919 = l;
        double r696920 = r696918 * r696919;
        double r696921 = 1.0;
        double r696922 = F;
        double r696923 = r696921 / r696922;
        double r696924 = tan(r696920);
        double r696925 = r696923 * r696924;
        double r696926 = r696925 * r696923;
        double r696927 = r696920 - r696926;
        return r696927;
}

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 8.5

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

  2. Simplified8.0

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

  4. Applied *-un-lft-identity8.0

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

  5. Applied times-frac0.6

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

  7. Applied div-inv0.7

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

  8. Applied associate-*r*0.7

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

  9. Final simplification0.7

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

Reproduce

herbie shell --seed 2019120 
(FPCore (F l)
  :name "VandenBroeck and Keller, Equation (6)"
  (- (* PI l) (* (/ 1 (* F F)) (tan (* PI l)))))